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Class 11 • Physics
Waves
Chapter-14
531 Questions
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52 Easy473 Medium6 Hard
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1
MediumAiims2019
A string wave equation is given $y=0.002 \sin (300 t-15 x) and mass density is (\mu=0.1 \mathrm{~kg} / \mathrm{m})$. Then find the tension force in the string.
Options:
A) 30 N
B) 20 N
C) 40 N
D) 45 N
2
MediumAiims2019
Two sources of sound S$_1 and S_2 are moving towards and away from a stationary observer with the same speed respectively. Observer detects 3 beats per second. Find speed of sources (approximately). Given, f_1=f_2=500$ Hz, speed of sound in air = 330 m/s
Options:
A) 1 m/s
B) 2 m/s
C) 3 m/s
D) 4 m/s
3
MediumAiims2019
If the speed of sound in air is 330 m/s then, find the number of tones present in an open organ pipe of length 1 m whose frequency is $\le$ 1000 Hz.
Options:
A) 2
B) 4
C) 8
D) 6
4
MediumAiims2018
A steel rod 100 cm long is damped at into middle. The fundamental frequency of longitudinal vibrations of the rod are given to be 2.53 kHz. What is the speed of sound in sound is steel?
Options:
A) 6.2 km/s
B) 5.06 km/s
C) 7.23 km/s
D) 7.45 km/s
5
MediumAiims2018
A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.
Options:
A) 12
B) 8
C) 6
D) 4
6
MediumAiims2018
Assertion To hear different beats difference of the frequencies of two sources should be less than 10. Reason More the number of beats more in the confusion.
Options:
A) Both Assertion and Reason are correct, Reason is the correct explanation of Assertion
B) Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
C) Assertion is correct and Reason is incorrect
D) Assertion is incorrect and Reason is correct
7
MediumAiims2017
The driver of a car travelling with speed $30 \mathrm{~ms}^{-1} towards a hill sounds a horn of frequency 600 \mathrm{~Hz}. If the velocity of sound in air is 330 \mathrm{~ms}^{-1}$, the frequency of reflected sound as heard by driver is :
Options:
A) 550 \mathrm{~Hz}
B) 555.5 \mathrm{~Hz}
C) 720 \mathrm{~Hz}
D) 500 \mathrm{~Hz}
8
MediumBITSAT2023
The fundamental frequency of an open organ pipe is $600 \mathrm{~Hz}. The first overtone of this pipe has same frequency as first overtone of a closed organ pipe. If speed of sound is 330 \mathrm{~m} / \mathrm{s}$, then the length of a closed organ pipe is
Options:
A) 21 cm
B) 37 cm
C) 31 cm
D) 80 cm
9
MediumBITSAT2023
The wavelength of two waves are 40 and $42 \mathrm{~cm} respectively. If the temperature of the room is 20^{\circ} \mathrm{C} then what will be the number of beats produced per second by these waves. When the speed of sound at 0^{\circ} \mathrm{C} is 332 \mathrm{~m} / \mathrm{s}$ ?
Options:
A) 34
B) 38
C) 44
D) None of these
10
MediumBITSAT2023
When a string is divided into four segments of $l_1, l_2, l_3 and l_4. The fundamental frequencies of these three segments are v_1, v_2, v_3 and v_4, respectively. The original fundamental frequency (v)$ of the string is
Options:
A) \sqrt{v}=\sqrt{v_1}+\sqrt{v_2}+\sqrt{v_3}+\sqrt{4}
B) v=v_1+v_2+v_3+v_4
C) 1 / v=1 / v_1+1 / v_2+1 / v_3+1 / v_4
D) \frac{1}{\sqrt{v}}=\frac{1}{\sqrt{v_1}}+\frac{1}{\sqrt{v_2}}+\frac{1}{\sqrt{v_3}}+\frac{1}{\sqrt{v_4}}
11
MediumBITSAT2022
In a resonance coloum first and second resonance are obtained at depths 24 cm and 78 cm the third resonance will be obtained at depth.
Options:
A) 160 m
B) 132 m
C) 131 m
D) 152 m
12
MediumBITSAT2022
A submarine A travelling at 17 m/s is being chased along the line of its velocity by another submarine B travelling at 34 m/s. B sends a sonar signal of 600 Hz to detect A and receives a reflected sound of frequency $\nu. The of \nu is [Speed of sound in water = 1500 ms-$1]
Options:
A) 613.7 Hz
B) 6137 Hz
C) 62 Hz
D) 539 Hz
13
MediumBITSAT2022
Transverse waves of the same frequency are generated in two steel wires A and B. The diameter of A is twice that of B and the tension in A is half that in B. The ratio of the velocities of the waves in A and B is
Options:
A) 1 : 2
B) 1 : $\sqrt2
C) 1 : 2$\sqrt2
D) 3 : 2$\sqrt2
14
MediumBITSAT2022
In the diagram shown below, both the strings AB and CD are made of same material and have same cross-section. The pulleys are light and fictionless. If the speed of wave in string AB is v1 and in CD is v2, then ${{{v_1}} \over {{v_2}}}$ is
Options:
A) 1
B) \sqrt2
C) 2
D) 1$\sqrt2
15
MediumBITSAT2021
The equation of progressive wave is given by $Y = \sin \left[ {x\left( {{t \over 5} - {x \over 9}} \right) + {\pi \over 6}} \right]$ cm. Which one of the following is correct?
Options:
A) v = 5 cm/s
B) \lambda$ = 18 cm
C) A = 0.04 cm
D) f = 50 Hz
16
MediumBITSAT2021
Two cars approach a stationary observer from opposite sides as shown in the figure. The observer hears no beats. If the frequency of the horn of the car B is 504 Hz, then the frequency of the horn of the car A will be
Options:
A) 529.2 Hz
B) 440.5 Hz
C) 295.2 Hz
D) None of these
17
MediumBITSAT2020
The vibrations of a string of length 60 cm fixed at both ends are represented by the equation $y = 4\sin \left( {{{\pi x} \over {15}}} \right)\cos (96\pi t)$ where x and y are in cm and t is in second. Calculate the velocity of the particle at x = 7.5 cm at t = 0.25 s.
Options:
A) 4 m/s
B) 0
C) 16 m/s
D) 9.8 m/s
18
MediumCOMEDK2025
The fundamental frequency of sound produced in an open pipe of length \mathbf{L}_1 is same as the frequency of the 3^{\text {rd }} harmonic of the sound produced in the closed pipe of length \mathbf{L}_2 Then the ratio of \frac{L_1}{L_2} is :
Options:
A) \frac{L_1}{L_2}=\frac{3}{1}
B) \frac{L_1}{L_2}=\frac{1}{3}
C) \frac{L_1}{L_2}=\frac{2}{3}
D) \frac{L_1}{L_2}=\frac{3}{2}
19
MediumCOMEDK2025
An open pipe is in second harmonic with frequency f_1. One end of the tube is closed and frequency is increased to f_2 and it resonates again with nth harmonic. For what value of n , the ratio of \frac{f_1}{f_2} is \frac{4}{5} ?
Options:
A) 3
B) 9
C) 5
D) 7
20
MediumCOMEDK2024
The number of possible natural oscillations of air column in a pipe closed at one end of length $85 \mathrm{~cm} whose frequencies lie below 1250 \mathrm{~Hz} are (velocity of sound =340 \mathrm{~ms}^{-1}$)
Options:
A) 6
B) 8
C) 4
D) 5
21
MediumCOMEDK2024
A tuning fork of unknown frequency produces 4 beats with tuning fork of frequency $310 \mathrm{~Hz}$. It gives the same number of beats on filing. The initial frequency of a tuning fork is
Options:
A) 620 Hz
B) 306 Hz
C) 314 Hz
D) 310 Hz
22
MediumCOMEDK2024
A string of length $25 \mathrm{~cm} and mass 10^{-3} \mathrm{~kg} is clamped at its ends. The tension in the string is 2.5 \mathrm{~N}. The identical wave pulses are generated at one end and at regular interval of time, \Delta \mathrm{t}. The minimum value of \Delta \mathrm{t}$, so that a constructive interference takes place between successive pulses is
Options:
A) 0.2 s
B) 1 s
C) 40 ms
D) 20 ms
23
MediumCOMEDK2023
With what velocity should an observer approach a stationary sound source, so that the apparent frequency of sound should appear double the actual frequency?
Options:
A) v / 2
B) 3 v
C) 2 v
D) v
24
MediumCOMEDK2023
A car is moving towards a high cliff. The car driver sounds a horn of frequency $f. The reflected sound heard by the driver has a frequency 2 f. If v$ be the velocity of sound, then the velocity of the car in the same velocity units, will be
Options:
A) \frac{v}{\sqrt{2}}
B) \frac{v}{3}
C) \frac{v}{4}
D) \frac{v}{2}
25
MediumCOMEDK2023
A string vibrates with a frequency of $200 \mathrm{~Hz}. When its length is doubled and tension is altered, it begins to vibrate with a frequency of 300 \mathrm{~Hz}$. The ratio of the new tension to the original tension is
Options:
A) 9 : 1
B) 1 : 9
C) 3 : 1
D) 1 : 3
26
MediumCOMEDK2023
Two open organ pipes A and B of length $22 \mathrm{~cm} and 22.5 \mathrm{~cm}$ respectively produce 2 beats per sec when sounded together. The frequency of the shorter pipe is
Options:
A) 92 Hz
B) 90 Hz
C) 88 Hz
D) 86 Hz
27
MediumCOMEDK2022
A bat emitting an ultrasonic wave of frequency 4.5 $\times$ 104 Hz at speed of 6 m/s between two parallel walls. The two frequencies heard by the bat will be
Options:
A) 4.67 $\times 104 Hz, 4.34 \times$ 104 Hz
B) 4.34 $\times 104 Hz, 4.67 \times$ 104 Hz
C) 4.5 $\times 104 Hz, 5.4 \times$ 104 Hz
D) 4.67 $\times 103 Hz, 4.34 \times$ 103 Hz
28
MediumCOMEDK2022
A source of sound emits sound waves at frequency $f_0. It is moving towards an observer with fixed speed {v_s} ({v_s},v, where v is the speed of sound in air.) If the observers were to move towards the source with speed v_0, one of the following two graphs (A and B) will give the correct variation of the frequency f heard by the observer as v_0 is changed. The variation of f with v_0$ is given correctly by
Options:
A) graph A with slope $ = {{{f_0}} \over {(v + {v_s})}}
B) graph B with slope $ = {{{f_0}} \over {(v - {v_s})}}
C) graph A with slope $ = {{{f_0}} \over {(v - {v_s})}}
D) graph B with slope $ = {{{f_0}} \over {(v + {v_s})}}
29
MediumCOMEDK2022
The string of length 2 m is fixed at both ends. If the string vibrates in its fourth normal mode with a frequency of 500 Hz, then the waves would travel on it with a velocity of
Options:
A) 125 m/s
B) 250 m/s
C) 500 m/s
D) 1000 m/s
30
MediumCOMEDK2021
The displacement of a wave is given by $y = 20\cos (\omega t + 4z)$ The amplitude of the given wave is
Options:
A) 10
B) 20
C) 20\sqrt2
D) 10\sqrt2
31
MediumCOMEDK2021
If frequencies are $(\nu-1) and (\nu+2)$, then find the value of beats.
Options:
A) 2
B) 1
C) 3
D) 4
32
MediumCOMEDK2020
The equation of a progressive wave can be given by $y=15\sin(660\pi t-0.02\pi x)$ cm. The frequency of the wave is
Options:
A) 330 Hz
B) 342 Hz
C) 365 Hz
D) 660 Hz
33
MediumCOMEDK2020
A source of sound gives 5 beats per second, when sounded with another source of frequency 100 s$^{-1}. The second harmonic of the source, together with a source of frequency 205 s^{-1}$ gives 5 beats per second. What is frequency of the source?
Options:
A) 95 s$^{-1}
B) 105 s$^{-1}
C) 100 s$^{-1}
D) 205 s$^{-1}
34
HardJee Advance2025
An audio transmitter (T) and a receiver (R) are hung vertically from two identical massless strings of length 8 m with their pivots well separated along the X axis. They are pulled from the equilibrium position in opposite directions along the X axis by a small angular amplitude \theta_0=\cos ^{-1}(0.9) and released simultaneously. If the natural frequency of the transmitter is 660 Hz and the speed of sound in air is 330 \mathrm{~m} / \mathrm{s}, the maximum variation in the frequency (in Hz ) as measured by the receiver (Take the acceleration due to gravity g=10 \mathrm{~m} / \mathrm{s}^2 ) is _____________.
Options:
35
EasyJee Advance2024
A source (S) of sound has frequency 240 \mathrm{~Hz}. When the observer (O) and the source move towards each other at a speed v with respect to the ground (as shown in Case 1 in the figure), the observer measures the frequency of the sound to be 288 \mathrm{~Hz}. However, when the observer and the source move away from each other at the same speed v with respect to the ground (as shown in Case 2 in the figure), the observer measures the frequency of sound to be n \mathrm{~Hz}. The value of n is ___________.
Options:
36
EasyJee Advance2023
A string of length 1 \mathrm{~m} and mass 2 \times 10^{-5} \mathrm{~kg} is under tension T. When the string vibrates, two successive harmonics are found to occur at frequencies 750 \mathrm{~Hz} and 1000 \mathrm{~Hz}. The value of tension T is ________ Newton.
Options:
37
MediumJee Advance2023
S_1 and S_2 are two identical sound sources of frequency 656 \mathrm{~Hz}. The source S_1 is located at O and S_2 moves anti-clockwise with a uniform speed 4 \sqrt{2} \mathrm{~m} \mathrm{~s}^{-1} on a circular path around O, as shown in the figure. There are three points P, Q and R on this path such that P and R are diametrically opposite while Q is equidistant from them. A sound detector is placed at point P. The source S_1 can move along direction O P. [Given: The speed of sound in air is 324 \mathrm{~m} \mathrm{~s}^{-1} ]
Options:
38
MediumJee Advance2023
S_1 and S_2 are two identical sound sources of frequency 656 \mathrm{~Hz}. The source S_1 is located at O and S_2 moves anti-clockwise with a uniform speed 4 \sqrt{2} \mathrm{~m} \mathrm{~s}^{-1} on a circular path around O, as shown in the figure. There are three points P, Q and R on this path such that P and R are diametrically opposite while Q is equidistant from them. A sound detector is placed at point P. The source S_1 can move along direction O P. [Given: The speed of sound in air is 324 \mathrm{~m} \mathrm{~s}^{-1} ]
Options:
39
MediumJee Advance2020
A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of 2 ms−1 in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is 320 ms−1, the smallest value of the percentage change required in the length of the pipe is ____________.
Options:
40
MediumJee Advance2019
A train S1, moving with a uniform velocity of 108 km/h, approaches another train S2 standing on a platform. An observer O moves with a uniform velocity of 36 km/h towards S2, as shown in figure. Both the trains are blowing whistles of same frequency 120 Hz. When O is 600 m away from S2 and distance between S1 and S2 is 800 m, the number of beats heard by O is ............ . [Speed of the sound = 330 m/s ............ .]
Options:
41
MediumJee Advance2018
Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed $1.0\,m{s^{ - 1}} and the man behind walks at a speed 2.0\,m{s^{ - 1}}. A third man in standing at a height 12 m above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency 1430 Hz. The speed of sound in air is 330\,m{s^{ - 1}}. At the instant, when the moving men are 10 m apart, the stationary man is equidistant from them. The frequency of beats in Hz,$ heard by the stationary man at this instant, is _____________.
Options:
42
MediumJee Advance2017
A stationary source emits sound of frequency ${f_0} = 492\,Hz. The sound is reflected by a large car approaching the source with a speed of 2\,m{s^{ - 1.}} The reflected signal is received by the source and superposed with the original. What will be the beat frequency of the resulting signal in Hz? (Given that the speed of sound in air is 330\,m{s^{ - 1}}$ and the car reflects the sound at the frequency it has received).
Options:
43
MediumJee Advance2015
Four harmonic waves of equal frequencies and equal intensities I0 have phase angles 0, ${\pi \over 3},{{2\pi } \over 3} and \pi$. When they are superposed, the intensity of the resulting wave is nI0. The value of n is
Options:
44
MediumJee Advance2010
A stationary source is emitting sound at a fixed frequency f0, which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is 1.2% of f0. What is the difference in the speeds of the cars (in km per hour) to the nearest integer? The cars are moving at constant speeds much smaller than the speed of sound which is 330 ms$-$1.
Options:
45
EasyJee Advance2010
When two progressive waves ${y_1} = 4\sin (2x - 6t) and {y_2} = 3\sin \left( {2x - 6t - {\pi \over 2}} \right)$ are superimposed, the amplitude of the resultant wave is __________.
Options:
46
EasyJee Advance2009
A 20 cm long string, having a mass of 1.0 g, is fixed at both the ends. The tension in the string is 0.5 N. The string is set into vibrations using an external vibrator of frequency 100 Hz. find the separation (in cm) between the successive nodes on the string.
Options:
47
HardJee Advance2024
Two uniform strings of mass per unit length \mu and 4 \mu, and length L and 2 L, respectively, are joined at point \mathrm{O}, and tied at two fixed ends \mathrm{P} and \mathrm{Q}, as shown in the figure. The strings are under a uniform tension T. If we define the frequency v_0=\frac{1}{2 L} \sqrt{\frac{T}{\mu}}, which of the following statement(s) is(are) correct?
Options:
A) With a node at \mathrm{O}, the minimum frequency of vibration of the composite string is v_0.
B) With an antinode at \mathrm{O}, the minimum frequency of vibration of the composite string is 2 v_0.
C) When the composite string vibrates at the minimum frequency with a node at \mathrm{O}, it has 6 nodes, including the end nodes.
D) No vibrational mode with an antinode at \mathrm{O} is possible for the composite string.
48
MediumJee Advance2021
A source, approaching with speed u towards the open end of a stationary pipe of length L, is emitting a sound of frequency fs. The farther end of the pipe is closed. The speed of sound in air is v and f0 is the fundamental frequency of the pipe. For which of the following combination(s) of u and fs, will the sound reaching the pipe lead to a resonance?
Options:
A) u = 0.8v and fs = f0
B) u = 0.8v and fs = 2f0
C) u = 0.8v and fs = 0.5f0
D) u = 0.5v and fs = 1.5f0
49
HardJee Advance2018
In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency $500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm.$ Which of the following statements is (are) true?
Options:
A) The speed of second determined from this experiment is $332\,m{s^{ - 1}}
B) The end correction in this experiment is $0.9 cm
C) The wavelength of the sound wave is $66.4 cm
D) The resonance at $50.7 cm$ corresponds to the fundamental harmonic
50
HardJee Advance2017
A block $M hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to fixed rigid support at O. A transverse wave pulse (Pulse 1) of wavelength {\lambda _0} is produced at point O on the rope. The pulse takes time {T_{OA}} to reach point A. If the wave pulse of wavelength {\lambda _0} is produced at point A (Pulse 2) without disturbing the position of M it takes time {T_{AO}} to reach point O.$ which of the following options is/are correct?
Options:
A) The time ${T_{AO}} = {T_{OA}}
B) The velocities of the two pulses (Pulse 1 and Pulse 2) are the same at the midpoint of rope
C) The wavelength of Pulse 1 becomes longer when it reaches point $A
D) The velocity of any pulse along the rope is independent of its frequency and wavelength
51
HardJee Advance2016
Two loudspeakers M and N are located 20m apart and emit sound at frequencies 118 Hz and 121 Hz, respectively. A car in initially at a point P, 1800 m away from the midpoint Q of the line MN and moves towards Q constantly at 60 km/h along the perpendicular bisector of MN. It crosses Q and eventually reaches a point R, 1800 m away from Q.Let v(t) represent the beat frequency measured by a person sitting in the car at time t. Let vP, vQ and vR be the beat frequencies measured at locations P, Q and R respectively. The speed of sound in air is 330 ms$-$1. Which of the following statement(s) is (are) true regarding the sound heard by the person?
Options:
A) The plot below represents schematically the variation of beat frequency with time
B) The rate of change in beat frequency is maximum when the car passes through Q
C) vP + vR = 2vQ
D) The plot below represents schematically the variations of beat frequency with time
52
MediumJee Advance2014
One end of a taut string of length 3 m along the x-axis is fixed at x = 0. The speed of the waves in the string is 100 ms$-$1. The other end of the string is vibrating in the y-direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary wave is (are)
Options:
A) y(t) = A\sin {{\pi x} \over 6}\cos {{50\pi t} \over 3}
B) y(t) = A\sin {{\pi x} \over 3}\cos {{100\pi t} \over 3}
C) y(t) = A\sin {{5\pi x} \over 6}\cos {{250\pi t} \over 3}
D) y(t) = A\sin {{5\pi x} \over 2}\cos 250\pi t
53
MediumJee Advance2014
A student is performing an experiment using a resonance column and a tuning fork of frequency 244 s$-1. He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is (0.350 \pm 0.005) m, the gas in the tube is(Useful information : \sqrt {167RT} = 640 J1/2 mol-1/2; \sqrt {140RT} = 590 J1/2 mol-1/2. The molar mass M in grams is given in the options. Take the values of \sqrt {10/M} $ for each gas as given there.)
Options:
A) Neon $\left( {M = 20,\sqrt {{{10} \over {20}}} = {7 \over {10}}} \right)
B) Nitrogen $\left( {M = 28,\sqrt {{{10} \over {28}}} = {3 \over 5}} \right)
C) Oxygen $\left( {M = 32,\sqrt {{{10} \over {32}}} = {9 \over {16}}} \right)
D) Argon $\left( {M = 36,\sqrt {{{10} \over {36}}} = {{17} \over {32}}} \right)
54
MediumJee Advance2013
Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other. Wind blows along the road with velocity w. One of these vehicles blows a whistle of frequency f1. An observer in the other vehicle hears the frequency of the whistle to be f2. The speed of sound in still air is V. The correct statement(s) is(are)
Options:
A) If the wind blows from the observer to the source, f2 > f1.
B) If the wind blows from the source to the observer, f2 > f1.
C) If the wind blows from the observer to the source, f2 < f1
D) If the wind blows from the source to the observer, f2 < f1.
55
MediumJee Advance2013
A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation y(x, t) = (0.01 m) sin[(62.8 m$-1)x] cos[(628 s-1)t] Assuming \pi$ = 3.14, the correct statement(s) is(are)
Options:
A) The number of nodes is 5.
B) The length of the string is 0.25 m.
C) The maximum displacement of the mid-point of the string, from its equilibrium position is 0.01 m.
D) The fundamental frequency is 100 Hz.
56
EasyJee Advance2009
Under the influence of the Coulomb field of charge +Q, a charge $-$q is moving around it in an elliptical orbit. Find out the correct statement(s):
Options:
A) The angular momentum of the charge $-$q is constant.
B) The linear momentum of the charge $-$q is constant.
C) The angular velocity of the charge $-$q is constant.
D) The linear speed of the charge $-$q is constant.
57
EasyJee Advance2019
A musical instrument is made using four different metal strings, 1, 2, 3 and 4 with mass per unit length $\mu , 2\mu , 3\mu and 4\mu respectively. The instrument is played by vibrating the strings by varying the free length in between the range L0 and 2L0. It is found that in string-1\mu $ at free length L0 and tension T0 the fundamental mode frequency is f0.List-I gives the above four strings while list-II lists the magnitude of some quantity. If the tension in each string is T0, the correct match for the highest fundamental frequency in f0 units will be
Options:
A) I $ \to P, II \to Q, III \to T, IV \to $ S
B) I $ \to P, II \to R, III \to S, IV \to $ Q
C) I $ \to Q, II \to S, III \to R, IV \to $ P
D) I $ \to Q, II \to P, III \to R, IV \to $ T
58
MediumJee Advance2019
A musical instrument is made using four different metal strings, 1, 2, 3 and 4 with mass per unit length $\mu , 2\mu , 3\mu and 4\mu respectively. The instrument is played by vibrating the strings by varying the free length in between the range L0 and 2L0. It is found that in string-1\mu at free length L0 and tension T0 the fundamental mode frequency is f0.List-I gives the above four strings while list-II lists the magnitude of some quantity. The length of the strings 1, 2, 3 and 4 are kept fixed at L0, {{3{L_0}} \over 2}, {{5{L_0}} \over 4} and {{7{L_0}} \over 4}$ respectively. Strings 1, 2, 3 and 4 are vibrated at their 1st, 3rd, 5th and 14th harmonies, respectively such that all the strings have same frequency.The correct match for the tension in the four strings in the units of T0 will be
Options:
A) I $ \to P, II \to R, III \to T, IV \to $ U
B) I $ \to P, II \to Q, III \to R, IV \to $ T
C) I $ \to P, II \to Q, III \to T, IV \to $ U
D) I $ \to T, II \to Q, III \to R, IV \to $ U
59
MediumJee Advance2012
A student is performing the experiment of resonance Column. The diameter of the column tube is 4 cm. The frequency of the tuning fork is 512 Hz. The air temperature is 38oC in which the speed of sound is 336 m/s. The zero of the meter scale coincides with the top end of the Resonance Column tube. When the first resonance occurs, the reading of the water level in the column is
Options:
A) 14.0 cm
B) 15.2 cm
C) 16.4 cm
D) 17.6 cm
60
MediumJee Advance2011
A police car with a siren of frequency 8 kHz is moving with uniform velocity 36 km/hr towards a tall building which reflects the sound waves. The speed of sound in air is 320 m/s. The frequency of the siren heard by the car driver is
Options:
A) 8.50 kHz
B) 8.25 kHz
C) 7.75 kHz
D) 7.50 kHz
61
MediumJee Advance2011
Column I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as $\lambda$f. Match each system with statements given in Column II describing the nature and wavelength of the standing waves :
Options:
A) (A)$\to(T); (B)\to(P), (S); (C)\to(Q), (S); (D)\to$(Q)
B) (A)$\to(P), (T); (B)\to(P); (C)\to(Q), (S); (D)\to$(Q)
C) (A)$\to(P); (B)\to(P), (S); (C)\to(Q); (D)\to$(Q), (R)
D) (A)$\to(P), (T); (B)\to(P), (S); (C)\to(Q), (S); (D)\to$(Q), (R)
62
MediumJee Advance2010
A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is 50 N and the speed of sound is 320 ms−1, the mass of the string is
Options:
A) 5 grams
B) 10 grams
C) 20 grams
D) 40 grams
63
MediumJee Advance2008
A transverse sinusoidal wave moves along a string in the positive x-direction at a speed of 10 cm/s. The wavelength of the waves is 0.5 m and its amplitude is 10 cm. At a particular time t, the snap-shot of the wave is shown in figure. The velocity of point P when its displacement is 5 cm is :
Options:
A) {{\sqrt {3\pi } } \over {50}}\widehat j$ m/s
B) - {{\sqrt {3\pi } } \over {50}}\widehat j$ m/s
C) {{\sqrt {3\pi } } \over {50}}\widehat i$ m/s
D) - {{\sqrt {3\pi } } \over {50}}\widehat i$ m/s
64
MediumJee Advance2008
A vibrating string of certain length 1 under a tension T resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length 75 cm inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency n. Now when the tension of the string is slightly increased the number of beats reduces to 2 per second. Assuming the velocity of sound in air to be 340 m/s, the frequency n of the tuning fork in Hz is:
Options:
A) 344
B) 336
C) 117.3
D) 109.3
65
EasyJee Advance2007
In the experiment to determine the speed of sound using a resonance column,
Options:
A) prongs of the tuning fork are kept in a vertical plane
B) prongs of the tuning fork are kept in a horizontal plane
C) in one of the two resonances observed, the length of the resonating air column is close to the wavelength of sound in air
D) in one of the two resonances observed, the length of the resonating air column is close to half of the wavelength of sound in air
66
MediumJee Advance2007
Two trains $A and B are moving with speeds 20 \mathrm{~m} / \mathrm{s} and 30 \mathrm{~m} / \mathrm{s} respectively in the same direction on the same straight track, with B ahead of A. The engines are at the front ends. The engines of train A blows a long whistle. Assume that the sound of the whistle is composed of components varying in frequency from f_{1}=800 \mathrm{~Hz} to f_{2}=1120 \mathrm{~Hz}, as shown in the figure. The spread in the frequency (highest frequency - lowest frequency) is thus 320 \mathrm{~Hz}. The speed of sound in still air is 340 \mathrm{~m} / \mathrm{s}$.
Options:
A) 340 \mathrm{~m} / \mathrm{s} for passengers in \mathrm{A} and 310 \mathrm{~m} / \mathrm{s} for passengers in \mathrm{B}
B) 360 \mathrm{~m} / \mathrm{s} for passengers in \mathrm{A} and 310 \mathrm{~m} / \mathrm{s} for passengers in \mathrm{B}
C) 310 \mathrm{~m} / \mathrm{s} for passengers in \mathrm{A} and 360 \mathrm{~m} / \mathrm{s} for passengers in \mathrm{B}
D) 340 \mathrm{~m} / \mathrm{s}$ for passengers in both the trains
67
MediumJee Advance2007
Two trains $A and B are moving with speeds 20 \mathrm{~m} / \mathrm{s} and 30 \mathrm{~m} / \mathrm{s} respectively in the same direction on the same straight track, with B ahead of A. The engines are at the front ends. The engines of train A blows a long whistle. Assume that the sound of the whistle is composed of components varying in frequency from f_{1}=800 \mathrm{~Hz} to f_{2}=1120 \mathrm{~Hz}, as shown in the figure. The spread in the frequency (highest frequency - lowest frequency) is thus 320 \mathrm{~Hz}. The speed of sound in still air is 340 \mathrm{~m} / \mathrm{s}$.
Options:
A)
B)
C)
D)
68
MediumJee Advance2007
Two trains $A and B are moving with speeds 20 \mathrm{~m} / \mathrm{s} and 30 \mathrm{~m} / \mathrm{s} respectively in the same direction on the same straight track, with B ahead of A. The engines are at the front ends. The engines of train A blows a long whistle. Assume that the sound of the whistle is composed of components varying in frequency from f_{1}=800 \mathrm{~Hz} to f_{2}=1120 \mathrm{~Hz}, as shown in the figure. The spread in the frequency (highest frequency - lowest frequency) is thus 320 \mathrm{~Hz}. The speed of sound in still air is 340 \mathrm{~m} / \mathrm{s}$.
Options:
A) 310 Hz
B) 330 Hz
C) 350 Hz
D) 290 Hz
69
MediumJee Advance2007
Column I describe some situations in which a small object moves. Column II describes some characteristics of these motions. Match the situation in Column I with the characteristics in Column II and indicate your answer by darkening appropriate bubbles in the $4 \times 4 matrix given in the ORS. Column I Column II (A) The object moves on the x-axis under a conservative force in such a way that its "speed" and "position" satisfy v = {c_1}\sqrt {{c_2} - {x^2}} , where c_1 and c_2 are positive constants. (P) The object executes a simple harmonic motion. (B) The object moves on the x-axis in such a way that its velocity and its displacement from the origin satisfy v=-kx, where k is a positive constant. (Q) The object does not change its direction. (C) The object is attached to one end of a massless spring of a given spring constant. The other end of the spring is attached to the ceiling of an elevator. Initially everything is at rest. The elevator starts going upwards with a constant acceleration a. The motion of the object is observed from the elevator during the period it maintains this acceleration. (R) The kinetic energy of the object keeps on decreasing (D) The object is projected from the earth's surface vertically upwards with a speed 2\sqrt {GMe/{\mathop{\rm Re}\nolimits} } , where, M_e is the mass of the earth and R_e$ is the radius of the earth. Neglect forces from objects other than the earth. (S) The object can change its direction only once.
Options:
A) [\mathrm{A} \rightarrow(\mathrm{P}); \mathrm{B} \rightarrow(\mathrm{Q}, \mathrm{R}); \mathrm{C} \rightarrow(\mathrm{P}); \mathrm{D} \rightarrow(\mathbf{Q}, \mathrm{R})]
B) [\mathrm{A} \rightarrow(\mathrm{Q, R}); \mathrm{B} \rightarrow(\mathrm{Q}, \mathrm{R}); \mathrm{C} \rightarrow(\mathrm{P}); \mathrm{D} \rightarrow(\mathbf{S}, \mathrm{R})]
C) [\mathrm{A} \rightarrow(\mathrm{P, S}); \mathrm{B} \rightarrow(\mathrm{Q}, \mathrm{R}); \mathrm{C} \rightarrow(\mathrm{P}); \mathrm{D} \rightarrow(\mathbf{R})]
D) [\mathrm{A} \rightarrow(\mathrm{P, R}); \mathrm{B} \rightarrow(\mathrm{Q}, \mathrm{R}); \mathrm{C} \rightarrow(\mathrm{P}); \mathrm{D} \rightarrow(\mathbf{S})]
70
MediumJee Advance2006
A massless rod is suspended by two identical strings AB and CD of equal length. A block of mass m is suspended from point O such that BO is equal to x. Further, it is observed that the frequency of 1st harmonic (fundamental frequency) in AB is equal to 2 nd harmonic frequency in CD. Then, length of BO is
Options:
A) \frac{\mathrm{L}}{5}
B) \frac{4 \mathrm{~L}}{5}
C) \frac{3 \mathrm{~L}}{4}
D) \frac{\mathrm{L}}{4}
71
MediumJee Advance2006
Two waves y_1=\mathrm{A} \cos (0.5 \pi x-100 \pi t) and y_2=\mathrm{A} \cos (0.467 \pi x-92 \pi t) are travelling in a pipe placed along x-axis.
Options:
A) 4
B) 6
C) 8
D) 10
72
MediumJee Advance2006
Two waves y_1=\mathrm{A} \cos (0.5 \pi x-100 \pi t) and y_2=\mathrm{A} \cos (0.467 \pi x-92 \pi t) are travelling in a pipe placed along x-axis.
Options:
A) 100 \mathrm{~m} / \mathrm{s}
B) 192 \mathrm{~m} / \mathrm{s}
C) 200 \mathrm{~m} / \mathrm{s}
D) 96 \mathrm{~m} / \mathrm{s}
73
MediumJee Advance2006
Two waves y_1=\mathrm{A} \cos (0.5 \pi x-100 \pi t) and y_2=\mathrm{A} \cos (0.467 \pi x-92 \pi t) are travelling in a pipe placed along x-axis.
Options:
A) 100
B) 46
C) 192
D) 96
74
MediumJee Advance2005
A whistling train approaches a junction. An observer standing at the junction observes the frequency to be 2.2 kHz and 1.8 kHz of the approaching and the receding train. Find the speed of the train (speed of sound = 300 m/s).
Options:
A) 30
B) 20
C) 60
D) 75
75
MediumJee Advance2005
A transverse harmonic disturbance is produced in a string. The maximum transverse velocity is 3 m/s and the maximum transverse acceleration is 90 m/s$^2$ . If the wave velocity is 20 m/s, then find the waveform.
Options:
A) [y=(0.45) \sin \{[(30) t \pm(1.5) x] \pm \phi\}]
B) [y=(0.5) \sin \{[(50) t \pm(2.5) x] \pm \phi\}]
C) [y=(0.1) \sin \{[(30) t \pm(1.5) x] \pm \phi\}]
D) [y=(0.2) \sin \{[(60) t \pm(1.5) x] \pm \phi\}]
76
MediumJEE Mains2026
Two tuning forks A and B are sounded together giving rise to 8 beats in 2 s. When fork A is loaded with wax, the beat frequency is reduced to 4 beats in 2 s. If the original frequency of tuning fork B is 380 Hz then original frequency of tuning fork A is _________ Hz.
Options:
77
MediumJEE Mains2026
The velocity of sound in air is doubled when the temperature is raised from 0^{\circ} \mathrm{C} to \alpha{ }^{\circ} \mathrm{C}. The value of \alpha is \_\_\_\_ .
Options:
78
MediumJEE Mains2026
Two loudspeakers \left(L_1\right. and \left.L_2\right) are placed with a separation of 10 m , as shown in figure. Both speakers are fed with an audio input signal of same frequency with constant volume. A voice recorder, initially at point A, at equidistance to both loud speakers, is moved by 25 m along the line A B while monitoring the audio signal. The measured signal was found to undergo 10 cycles of minima and maxima during the movement. The frequency of the input signal is \_\_\_\_ Hz (Speed of sound in air is 324 \mathrm{~m} / \mathrm{s} and \sqrt{5}=2.23 )
Options:
79
MediumJEE Mains2024
A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $\left(\frac{a-1}{a}\right) then the value of a$ is _________.
Options:
80
EasyJEE Mains2024
Two open organ pipes of lengths $60 \mathrm{~cm} and 90 \mathrm{~cm} resonate at 6^{\text {th }} and 5^{\text {th }} harmonics respectively. The difference of frequencies for the given modes is _________ \mathrm{Hz}. (Velocity of sound in air =333 \mathrm{~m} / \mathrm{s}$)
Options:
81
EasyJEE Mains2024
A sonometer wire of resonating length $90 \mathrm{~cm} has a fundamental frequency of 400 \mathrm{~Hz} when kept under some tension. The resonating length of the wire with fundamental frequency of 600 \mathrm{~Hz} under same tension _______ \mathrm{cm}$.
Options:
82
MediumJEE Mains2024
A tuning fork resonates with a sonometer wire of length 1 \mathrm{~m} stretched with a tension of 6 \mathrm{~N}. When the tension in the wire is changed to 54 \mathrm{~N}, the same tuning fork produces 12 beats per second with it. The frequency of the tuning fork is ________________ \mathrm{Hz}.
Options:
83
EasyJEE Mains2024
A point source is emitting sound waves of intensity $16 \times 10^{-8} \mathrm{~Wm}^{-2} at the origin. The difference in intensity (magnitude only) at two points located at a distances of 2 m and 4 m from the origin respectively will be _________ \times 10^{-8} \mathrm{~Wm}^{-2}$.
Options:
84
MediumJEE Mains2024
In a closed organ pipe, the frequency of fundamental note is $30 \mathrm{~Hz}. A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to 110 \mathrm{~Hz}. If the organ pipe has a cross-sectional area of 2 \mathrm{~cm}^2, the amount of water poured in the organ tube is __________ g. (Take speed of sound in air is 330 \mathrm{~m} / \mathrm{s}$)
Options:
85
MediumJEE Mains2024
A closed organ pipe $150 \mathrm{~cm} long gives 7 beats per second with an open organ pipe of length 350 \mathrm{~cm}, both vibrating in fundamental mode. The velocity of sound is __________ \mathrm{m} / \mathrm{s}$.
Options:
86
EasyJEE Mains2023
The fundamental frequency of vibration of a string stretched between two rigid support is 50 \mathrm{~Hz}. The mass of the string is 18 \mathrm{~g} and its linear mass density is 20 \mathrm{~g} / \mathrm{m}. The speed of the transverse waves so produced in the string is ___________ \mathrm{ms}^{-1}
Options:
87
EasyJEE Mains2023
In an experiment with sonometer when a mass of $180 \mathrm{~g} is attached to the string, it vibrates with fundamental frequency of 30 \mathrm{~Hz}. When a mass \mathrm{m} is attached, the string vibrates with fundamental frequency of 50 \mathrm{~Hz}. The value of \mathrm{m}$ is ___________ g.
Options:
88
MediumJEE Mains2023
For a certain organ pipe, the first three resonance frequencies are in the ratio of $1:3:5 respectively. If the frequency of fifth harmonic is 405 \mathrm{~Hz} and the speed of sound in air is 324 \mathrm{~ms}^{-1} the length of the organ pipe is _________ \mathrm{m}$.
Options:
89
EasyJEE Mains2023
The equation of wave is given by $\mathrm{Y}=10^{-2} \sin 2 \pi(160 t-0.5 x+\pi / 4) where x and Y are in \mathrm{m} and \mathrm{t} in s. The speed of the wave is ________ \mathrm{km} ~\mathrm{h}^{-1}$.
Options:
90
EasyJEE Mains2023
A transverse harmonic wave on a string is given by $y(x,t) = 5\sin (6t + 0.003x) where x and y are in cm and t in sec. The wave velocity is _______________ ms^{-1}$.
Options:
91
EasyJEE Mains2023
A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental frequency of 180 Hz will be _________ cm.
Options:
92
EasyJEE Mains2023
An organ pipe $40 \mathrm{~cm} long is open at both ends. The speed of sound in air is 360 \mathrm{~ms}^{-1}. The frequency of the second harmonic is ___________ \mathrm{Hz}$.
Options:
93
EasyJEE Mains2023
A person driving car at a constant speed of $15 \mathrm{~m} / \mathrm{s} is approaching a vertical wall. The person notices a change of 40 \mathrm{~Hz} in the frequency of his car's horn upon reflection from the wall. The frequency of horn is _______________ \mathrm{Hz}. (Given: Speed of sound : 330 \mathrm{~m} / \mathrm{s}$ )
Options:
94
MediumJEE Mains2023
The displacement equations of two interfering waves are given by y_{1}=10 \sin \left(\omega t+\frac{\pi}{3}\right) \mathrm{cm}, y_{2}=5[\sin \omega t+\sqrt{3} \cos \omega t] \mathrm{cm} respectively. The amplitude of the resultant wave is _______ \mathrm{cm}.
Options:
95
EasyJEE Mains2023
Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm. The phase difference between the individual waves is _________ degree.
Options:
96
EasyJEE Mains2023
A train blowing a whistle of frequency 320 Hz approaches an observer standing on the platform at a speed of 66 m/s. The frequency observed by the observer will be (given speed of sound = 330 ms$^{-1}$) __________ Hz.
Options:
97
MediumJEE Mains2023
The distance between two consecutive points with phase difference of 60$^\circ$ in a wave of frequency 500 Hz is 6.0 m. The velocity with which wave is travelling is __________ km/s
Options:
98
EasyJEE Mains2022
The frequency of echo will be __________ Hz if the train blowing a whistle of frequency 320 Hz is moving with a velocity of 36 km/h towards a hill from which an echo is heard by the train driver. Velocity of sound in air is 330 m/s.
Options:
99
MediumJEE Mains2022
A wire of length 30 cm, stretched between rigid supports, has it's nth and (n + 1)th harmonics at 400 Hz and 450 Hz, respectively. If tension in the string is 2700 N, it's linear mass density is ____________ kg/m.
Options:
100
MediumJEE Mains2022
When a car is approaching the observer, the frequency of horn is $100 \mathrm{~Hz}. After passing the observer, it is 50 \mathrm{~Hz}. If the observer moves with the car, the frequency will be \frac{x}{3} \mathrm{~Hz} where x=$ ________________.
Options:
101
EasyJEE Mains2022
Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the $\sqrt3$ times of amplitude of individual motions. The phase difference between the two motions is ___________ (degree).
Options:
102
HardJEE Mains2022
An observer is riding on a bicycle and moving towards a hill at $18 \,\mathrm{kmh}^{-1}. He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is 640 \mathrm{~Hz} and velocity of the sound in air is 320 \mathrm{~m} / \mathrm{s}, the beat frequency between the two sounds heard by observer will be _____________ \mathrm{Hz}$.
Options:
103
MediumJEE Mains2022
An employee of a factory moving away from his workplace by a car listens to the siren of the factory. He drives the car at the speed of 72 kmh$-1 in the direction of wind which is blowing at 72 kmh-1 speed. Frequency of siren is 720 Hz. The employee hears an apparent frequency of ____________ Hz. (Assume speed of sound to be 340 ms-$1)
Options:
104
MediumJEE Mains2022
In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 cm for a tuning fork of frequency 400 Hz is used. The velocity of the sound at room temperature is 336 ms$-$1. The third resonance is observed when the air column has a length of _____________ cm.
Options:
105
MediumJEE Mains2022
A tunning fork of frequency 340 Hz resonates in the fundamental mode with an air column of length 125 cm in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is ___________ cm. (Velocity of sound in air is 340 ms$-$1)
Options:
106
EasyJEE Mains2022
A set of 20 tuning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is _________ Hz.
Options:
107
EasyJEE Mains2022
The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm. The length of the open organ pipe is _____________ cm.
Options:
108
EasyJEE Mains2022
Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by $y = (10\cos \pi x\sin {{2\pi t} \over T}) cm The amplitude of the particle at x = {4 \over 3}$ cm will be ___________ cm.
Options:
109
EasyJEE Mains2021
A wire having a linear mass density 9.0 $\times 10-$4 kg/m is stretched between two rigid supports with a tension of 900 N. The wire resonates at a frequency of 500 Hz. The next higher frequency at which the same wire resonates is 550 Hz. The length of the wire is ____________ m.
Options:
110
EasyJEE Mains2021
A tuning fork is vibrating at 250 Hz. The length of the shortest closed organ pipe that will resonate with the tuning fork will be __________ cm. (Take speed of sound in air as 340 ms$-$1)
Options:
111
EasyJEE Mains2021
Two cars X and Y are approaching each other with velocities 36 km/h and 72 km/h respectively. The frequency of a whistle sound as emitted by a passenger in car X, heard by the passenger in car Y is 1320 Hz. If the velocity of sound in air is 340 m/s, the actual frequency of the whistle sound produced is .................. Hz.
Options:
112
MediumJEE Mains2021
Two waves are simultaneously passing through a string and their equations are : y1 = A1 sin k(x $- vt), y2 = A2 sin k(x - vt + x0). Given amplitudes A1 = 12 mm and A2 = 5 mm, x0 = 3.5 cm and wave number k = 6.28 cm-$1. The amplitude of resulting wave will be ................ mm.
Options:
113
EasyJEE Mains2021
A source and a detector move away from each other in absence of wind with a speed of 20 m/s with respect to the ground. If the detector detects a frequency of 1800 Hz of the sound coming from the source, then the original frequency of source considering speed of sound in air 340 m/s will be ............... Hz.
Options:
114
EasyJEE Mains2021
Two travelling waves produces a standing wave represented by equation,y = 1.0 mm cos(1.57 cm$-1) x sin(78.5 s-$1)t. The node closest to the origin in the region x > 0 will be at x = .............. cm.
Options:
115
MediumJEE Mains2021
The frequency of a car horn encountered a change from 400 Hz to 500 Hz, when the car approaches a vertical wall. If the speed of sound is 330 m/s. Then the speed of car is ___________ km/h.
Options:
116
EasyJEE Mains2021
The amplitude of wave disturbance propagating in the positive x-direction is given by $y = {1 \over {{{(1 + x)}^2}}} at time t = 0 and y = {1 \over {1 + {{(x - 2)}^2}}}$ at t = 1 s, where x and y are in metres. The shape of wave does not change during the propagation. The velocity of the wave will be ___________ m/s.
Options:
117
MediumJEE Mains2021
A closed organ pipe of length L and an open organ pipe contain gases of densities $\rho1 and \rho2 respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is {x \over 3}L\sqrt {{{{\rho _1}} \over {{\rho _2}}}} $ where x is ___________. (Round off to the Nearest Integer)
Options:
118
MediumJEE Mains2021
The mass per unit length of a uniform wire is 0.135 g/cm. A transverse wave of the form y = $- 0.21 sin (x + 30t) is produced in it, where x is in meter and t is in second. Then, the expected value of tension in the wire is x \times 10-$2 N. Value of x is _________. (Round off to the nearest integer)
Options:
119
EasyJEE Mains2021
The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4%, will be __________%.
Options:
120
MediumJEE Mains2021
Two cars are approaching each other at an equal speed of 7.2 km/hr. When they see each other, both blow horns having frequency of 676 Hz. The beat frequency heard by each driver will be ___________ Hz. [Velocity of sound in air is 340 m/s.]
Options:
121
MediumJEE Mains2020
A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ________ Hz.
Options:
122
EasyJEE Mains2026
The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is 5 / x. The value of x is \_\_\_\_
Options:
A) 3
B) 2
C) 4
D) 1
123
EasyJEE Mains2026
A point source is kept at the center of a spherically enclosed detector. If the volume of the detector increased by 8 times, the intensity will
Options:
A) increase by 64 times
B) decrease by 4 times
C) decrease by 8 times
D) increase by 8 times
124
EasyJEE Mains2026
In an open organ pipe \nu_3 and \nu_6 are 3^{\text {rd }} and 6^{\text {th }} harmonic frequencies, respectively. If \nu_6-\nu_3=2200 \mathrm{~Hz} then length of the pipe is \_\_\_\_ mm . (Take velocity of sound in air is 330 \mathrm{~m} / \mathrm{s}.)
Options:
A) 200
B) 225
C) 275
D) 250
125
MediumJEE Mains2026
Two strings (A, B) having linear densities \mu_A=2 \times 10^{-4} \mathrm{~kg} / \mathrm{m} and, \mu_B=4 \times 10^{-4} \mathrm{~kg} / \mathrm{m} and lengths L_A=2.5 \mathrm{~m} and L_B=1.5 \mathrm{~m} respectively are joined. Free ends of A and B are tied to two rigid supports C and D, respectively creating a tension of 500 N in the wire. Two identical pulses, sent from C and D ends, take time t_1 and t_2, respectively, to reach the joint. The ratio t_1 / t_2 is:
Options:
A) 1.90
B) 1.18
C) 1.08
D) 1.67
126
MediumJEE Mains2025
The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, y_1(x, t) = 4 \sin (kx - \omega t) and y_2(x, t) = 2 \sin (kx - \omega t + \frac{2\pi}{3}), are: (Take the angular frequency of initial waves same as \omega)
Options:
A) \left[\sqrt{3}, \frac{\pi}{6}\right]
B) \left[2\sqrt{3}, \frac{\pi}{6}\right]
C) \left[6, \frac{2\pi}{3}\right]
D) \left[6, \frac{\pi}{3}\right]
127
MediumJEE Mains2025
Two strings with circular cross section and made of same material, are stretched to have same amount of tension. A transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section R is v_1, and that in the other string having radius of cross section R/2 is v_2. Then \frac{v_2}{v_1} =
Options:
A) 8
B) 4
C) 2
D) \sqrt{2}
128
MediumJEE Mains2025
The equation of a wave travelling on a string is y = sin[20πx + 10πt], where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is :
Options:
A) 10 cm
B) 2.5 cm
C) 20 cm
D) 5.0 cm
129
MediumJEE Mains2025
Two harmonic waves moving in the same direction superimpose to form a wave x=\mathrm{a} \cos (1.5 \mathrm{t}) \cos (50.5 \mathrm{t}) where t is in seconds. Find the period with which they beat. (close to nearest integer)
Options:
A) 1 s
B) 4 s
C) 2 s
D) 6 s
130
EasyJEE Mains2025
Displacement of a wave is expressed as x(t)=5 \cos \left(628 t+\frac{\pi}{2}\right) \mathrm{m}. The wavelength of the wave when its velocity is 300 \mathrm{~m} / \mathrm{s} is : $(\pi=3.14)
Options:
A) 0.33 m
B) 0.5 m
C) 3 m
D) 5 m
131
MediumJEE Mains2025
In an experiment with a closed organ pipe, it is filled with water by \left(\frac{1}{5}\right) th of its volume. The frequency of the fundamental note will change by
Options:
A) 20 \%
B) 25 \%
C) -20 \%
D) -25 \%
132
MediumJEE Mains2025
In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is:
Options:
A) 370 \mathrm{~m} / \mathrm{s}
B) 340 \mathrm{~m} / \mathrm{s}
C) 335 \mathrm{~m} / \mathrm{s}
D) 360 \mathrm{~m} / \mathrm{s}
133
MediumJEE Mains2025
A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the x-direction in 0.3 sec . The crest P is at x=0 at \mathrm{t}=0 \mathrm{sec} and maximum displacement of the wave is 2 cm . Which equation correctly represents this wave?
Options:
A) y=2 \cos (0.83 x-3.35 t) \mathrm{cm}
B) y=2 \sin (0.83 x-3.5 \mathrm{t}) \mathrm{cm}
C) y=2 \cos (0.13 x-0.5 t) \mathrm{cm}
D) y=2 \cos (3.35 x-0.83 \mathrm{t}) \mathrm{cm}
134
EasyJEE Mains2025
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason \mathbf{R} Assertion A: A sound wave has higher speed in solids than gases. Reason R: Gases have higher value of Bulk modulus than solids. In the light of the above statements, choose the correct answer from the options given below
Options:
A) Both \mathbf{A} and \mathbf{R} are true and \mathbf{R} is the correct explanation of \mathbf{A}
B) \mathbf{A} is false but \mathbf{R} is true
C) \mathbf{A} is true but \mathbf{R} is false
D) Both \mathbf{A} and \mathbf{R} are true but \mathbf{R} is NOT the correct explanation of \mathbf{A}
135
EasyJEE Mains2025
The equation of a transverse wave travelling along a string is y(x, t)=4.0 \sin \left[20 \times 10^{-3} x+600 t\right] \mathrm{mm}, where x is in mm and t is in second. The velocity of the wave is :
Options:
A) -60 \mathrm{~m} / \mathrm{s}
B) +60 \mathrm{~m} / \mathrm{s}
C) +30 \mathrm{~m} / \mathrm{s}
D) -30 \mathrm{~m} / \mathrm{s}
136
MediumJEE Mains2025
A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities \rho_1 and \rho_2, respectively. The frequency of 9^{\text {th }} harmonic of closed tube is identical with 4^{\text {th }} harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is \rho_1: \rho_2=1: 16, then the length of the open tube is :
Options:
A) \frac{15}{7} \mathrm{~cm}
B) \frac{20}{9} \mathrm{~cm}
C) \frac{20}{7} \mathrm{~cm}
D) \frac{15}{9} \mathrm{~cm}
137
EasyJEE Mains2024
A plane progressive wave is given by $y=2 \cos 2 \pi(330 \mathrm{t}-x) \mathrm{m}$. The frequency of the wave is :
Options:
A) 660 Hz
B) 340 Hz
C) 330 Hz
D) 165 Hz
138
EasyJEE Mains2024
The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is $60 \mathrm{~cm}$, the length of the closed pipe will be:
Options:
A) 15 cm
B) 60 cm
C) 45 cm
D) 30 cm
139
EasyJEE Mains2023
A car P travelling at $20 \mathrm{~ms}^{-1} sounds its horn at a frequency of 400 \mathrm{~Hz}. Another car \mathrm{Q} is travelling behind the first car in the same direction with a velocity 40 \mathrm{~ms}^{-1}. The frequency heard by the passenger of the car \mathrm{Q} is approximately [Take, velocity of sound =360 \mathrm{~ms}^{-1}$ ]
Options:
A) 485 Hz
B) 514 Hz
C) 421 Hz
D) 471 Hz
140
MediumJEE Mains2023
For a periodic motion represented by the equation $y=\sin \omega \mathrm{t}+\cos \omega \mathrm{t}$ the amplitude of the motion is
Options:
A) 1
B) \sqrt2
C) 0.5
D) 2
141
EasyJEE Mains2023
The engine of a train moving with speed $10 \mathrm{~ms}^{-1} towards a platform sounds a whistle at frequency 400 \mathrm{~Hz}. The frequency heard by a passenger inside the train is: (neglect air speed. Speed of sound in air =330 \mathrm{~ms}^{-1}$ )
Options:
A) 200 Hz
B) 412 Hz
C) 400 Hz
D) 388 Hz
142
EasyJEE Mains2023
A steel wire with mass per unit length $7.0 \times 10^{-3} \mathrm{~kg} \mathrm{~m}^{-1} is under tension of 70 \mathrm{~N}$. The speed of transverse waves in the wire will be:
Options:
A) 10 \mathrm{~m} / \mathrm{s}
B) 50 \mathrm{~m} / \mathrm{s}
C) 100 \mathrm{~m} / \mathrm{s}
D) 200 \pi\mathrm{~m} / \mathrm{s}
143
EasyJEE Mains2023
A person observes two moving trains, 'A' reaching the station and 'B' leaving the station with equal speed of $30 \mathrm{~m} / \mathrm{s}. If both trains emit sounds with frequency 300 \mathrm{~Hz}, (Speed of sound: 330 \mathrm{~m} / \mathrm{s}$) approximate difference of frequencies heard by the person will be:
Options:
A) 10 Hz
B) 55 Hz
C) 80 Hz
D) 33 Hz
144
EasyJEE Mains2023
A travelling wave is described by the equation $y(x,t) = [0.05\sin (8x - 4t)]$ m The velocity of the wave is : [all the quantities are in SI unit]
Options:
A) \mathrm{4~ms^{-1}}
B) \mathrm{2~ms^{-1}}
C) \mathrm{8~ms^{-1}}
D) \mathrm{0.5~ms^{-1}}
145
EasyJEE Mains2022
In the wave equation $ y=0.5 \sin \frac{2 \pi}{\lambda}(400 \mathrm{t}-x) \,\mathrm{m} $ the velocity of the wave will be:
Options:
A) 200 m/s
B) 200$\sqrt2$ m/s
C) 400 m/s
D) 400$\sqrt2$ m/s
146
EasyJEE Mains2022
A transverse wave is represented by $y=2 \sin (\omega t-k x)\, \mathrm{cm}. The value of wavelength (in \mathrm{cm}$) for which the wave velocity becomes equal to the maximum particle velocity, will be :
Options:
A) 4$\pi
B) 2$\pi
C) \pi
D) 2
147
EasyJEE Mains2022
Which of the following equations correctly represents a travelling wave having wavelength $\lambda$ = 4.0 cm, frequency v = 100 Hz and travelling in positive x-axis direction?
Options:
A) y = A\sin [(0.50\,\pi \,c{m^{ - 1}})x - (100\,\pi \,{s^{ - 1}})t]
B) y = A\sin \,\,2\pi [(0.25\,\,c{m^{ - 1}})x - (50\,{s^{ - 1}})t]
C) y = A\sin \left[ {\left( {{{2\pi } \over 4}\,c{m^{ - 1}}} \right)x - \left( {{{2\pi } \over {100}}\,{s^{ - 1}}} \right)t} \right]
D) y = A\sin \,\pi [(0.5\,\,c{m^{ - 1}})x - (200\,\,{s^{ - 1}})t]
148
MediumJEE Mains2022
A longitudinal wave is represented by $x = 10\sin 2\pi \left( {nt - {x \over \lambda }} \right)$ cm. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to :
Options:
A) 2$\pi
B) 5$\pi
C) \pi
D) {{5\pi } \over 2}
149
MediumJEE Mains2022
The velocity of sound in a gas, in which two wavelengths 4.08 m and 4.16 m produce 40 beats in 12s, will be :
Options:
A) 282.8 ms$-$1
B) 175.5 ms$-$1
C) 353.6 ms$-$1
D) 707.2 ms$-$1
150
EasyJEE Mains2022
If a wave gets refracted into a denser medium, then which of the following is true?
Options:
A) wavelength, speed and frequency decreases.
B) wavelength increases, sped decreases and frequency remains constant.
C) wavelength and speed decreases but frequency remains constant.
D) wavelength, speed and frequency increases.
151
EasyJEE Mains2022
An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency will be :
Options:
A) 20%
B) 10%
C) 5%
D) 0%
152
EasyJEE Mains2022
The equations of two waves are given by : y1 = 5 sin 2$\pi(x - vt) cm y2 = 3 sin 2\pi(x -$ vt + 1.5) cm These waves are simultaneously passing through a string. The amplitude of the resulting wave is :
Options:
A) 2 cm
B) 4 cm
C) 5.8 cm
D) 8 cm
153
MediumJEE Mains2021
The motion of a mass on a spring, with spring constant K is as shown in figure.The equation of motion is given by x(t) = A sin$\omegat + B cos\omegat with \omega = \sqrt {{K \over m}} Suppose that at time t = 0, the position of mass is x(0) and velocity v(0), then its displacement can also be represented as x(t) = C cos(\omegat - \phi), where C and \phi$ are :
Options:
A) C = \sqrt {{{2v{{(0)}^2}} \over {{\omega ^2}}} + x{{(0)}^2}} ,\phi = {\tan ^{ - 1}}\left( {{{x(0)\omega } \over {2v(0)}}} \right)
B) C = \sqrt {{{v{{(0)}^2}} \over {{\omega ^2}}} + x{{(0)}^2}} ,\phi = {\tan ^{ - 1}}\left( {{{x(0)\omega } \over {v(0)}}} \right)
C) C = \sqrt {{{v{{(0)}^2}} \over {{\omega ^2}}} + x{{(0)}^2}} ,\phi = {\tan ^{ - 1}}\left( {{{v(0)} \over {x(0)\omega }}} \right)
D) C = \sqrt {{{2v{{(0)}^2}} \over {{\omega ^2}}} + x{{(0)}^2}} ,\phi = {\tan ^{ - 1}}\left( {{{v(0)} \over {x(0)\omega }}} \right)
154
EasyJEE Mains2021
A sound wave of frequency 245 Hz travels with the speed of 300 ms$-$1 along the positive x-axis. Each point of the wave moves to and from through a total distance of 6 cm. What will be the mathematical expression of this travelling wave?
Options:
A) Y(x, t) = 0.03 [ sin 5.1x $- (0.2 \times$ 103)t ]
B) Y(x, t) = 0.03 [ sin 5.1x $- (1.5 \times$ 103)t ]
C) Y(x, t) = 0.06 [ sin 5.1x $- (1.5 \times$ 103)t ]
D) Y(x, t) = 0.06 [ sin 0.8x $- (0.5 \times$ 103)t ]
155
MediumJEE Mains2021
A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340 Hz. When fork A is filed, the beat frequency decreases to 2 beats/s. What is the frequency of fork A?
Options:
A) 335 Hz
B) 345 Hz
C) 338 Hz
D) 342 Hz
156
MediumJEE Mains2021
A student is performing the experiment of resonance column. The diameter of the column tube is 6 cm. The frequency of the tuning fork is 504 Hz. Speed of the sound at the given temperature is 336 m/s. The zero of the metre scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is :
Options:
A) 13 cm
B) 18.4 cm
C) 16.6 cm
D) 14.8 cm
157
EasyJEE Mains2021
Which of the following equations represents a travelling wave?
Options:
A) y = Aexcos($\omegat - \theta$)
B) y = Ae$-x2(vt + \theta$)
C) y = A sin (15x $-$ 2t)
D) y = A sinx cos$\omega$t
158
MediumJEE Mains2020
A sound source S is moving along a straight track with speed v, and is emitting, sound of frequency v0 (see figure). An observer is standing at a finite distance, at the point O, from the track. The time variation of frequency heard by the observer is best represented by: (t0 represents the instant when the distance between the source and observer is minimum)
Options:
A)
B)
C)
D)
159
MediumJEE Mains2020
A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from 440 Hz to 480 Hz, when it gets reflected from the wall. If the speed of sound in air is 345 m/s, then the speed of the car is :
Options:
A) 36 km/hr
B) 54 km/hr
C) 24 km/hr
D) 18 km/hr
160
MediumJEE Mains2020
In a resonance tube experiment when the tube is filled with water up to a height of 17.0 cm from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of 24.5 cm. If the velocity of sound in air is 330 m/s, the tuning fork frequency is :
Options:
A) 2200 Hz
B) 3300 Hz
C) 1100 Hz
D) 550 Hz
161
MediumJEE Mains2020
Assume that the displacement(s) of air is proportional to the pressure difference ($\Delta p) created by a sound wave. Displacement (s) further depends on the speed of sound (v), density of air (\rho ) and the frequency (f). If \Delta p ~ 10 Pa, v ~ 300 m/s, \rho $ ~ 1 kg/m3 and f ~ 1000 Hz, then s will be of the order of (take the multiplicative constant to be 1) :
Options:
A) 1 mm
B) {3 \over {100}}$ mm
C) 10 mm
D) {1 \over {10}}$ mm
162
MediumJEE Mains2020
The driver of a bus approaching a big wall notices that the frequency of his bus's horn changes from 420 Hz to 490 Hz when he hears it after it gets reflected from the wall. Find the speed of the bus if speed of the sound is 330 ms–1.
Options:
A) 91 kmh–1
B) 81 kmh–1
C) 61 kmh–1
D) 71 kmh–1
163
MediumJEE Mains2020
For a transverse wave travelling along a straight line, the distance between two peaks (crests) is 5 m, while the distance between one crest and one trough is 1.5 m. The possible wavelengths (in m) of the are :
Options:
A) 1, 3, 5, .....
B) {1 \over 1},{1 \over 3},{1 \over 5},$ .....
C) 1, 2, 3, .....
D) {1 \over 2},{1 \over 4},{1 \over 6},
164
MediumJEE Mains2020
A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block of mass 2 kg is attached to its free end. A transverse short wavetrain of wavelength 6 cm is produced at the lower end of the rope. What is the wavelength of the wavetrain (in cm) when it reaches the top of the rope ?
Options:
A) 12
B) 3
C) 9
D) 6
165
MediumJEE Mains2020
Two identical strings X and Z made of same material have tension TX and TZ in them. If their fundamental frequencies are 450 Hz and 300 Hz, respectively, then the ratio TX/TZ is
Options:
A) 2.25
B) 0.44
C) 1.25
D) 1.5
166
MediumJEE Mains2020
A wire of length L and mass per unit length 6.0 × 10–3 kgm–1 is put under tension of 540 N. Two consecutive frequencies that it resonates at are : 420 Hz and 490 Hz. Then L in meters is :
Options:
A) 5.1 m
B) 2.1 m
C) 1.1 m
D) 8.1 m
167
MediumJEE Mains2020
Three harmonic waves having equal frequency $\nu and same intensity {I_0}, have phase angles 0, {\pi \over 4} and - {\pi \over 4}$ respectively. When they are superimposed the intensity of the resultant wave is close to :
Options:
A) 5.8 I0
B) 3 I0
C) 0.2 I0
D) I0
168
MediumJEE Mains2020
A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2.06 × 104 N. When the tension is changed to T, the velocity changed to v/2. The value of T is close to :
Options:
A) 30.5 × 104 N
B) 2.50 × 104 N
C) 10.2 × 102 N
D) 5.15 × 103 N
169
MediumJEE Mains2020
A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much less than the speed of sound). The observer hears 2 beats/sec. The oscillation frequency of each tuning fork is v0 = 1400 Hz and the velocity of sound in air is 350 m/s. The speed of each tuning fork is close to :
Options:
A) 1 m/s
B) {1 \over 8}$ m/s
C) {1 \over 4}$ m/s
D) {1 \over 2}$ m/s
170
MediumJEE Mains2020
Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm2) is 90 ms-1. If the Young's modulus of wire is 16 $ \times $ 1011 Nm-2, the extension of wire over its natural length is :
Options:
A) 0.03 mm
B) 0.04 mm
C) 0.02 mm
D) 0.01 mm
171
MediumJEE Mains2019
Two sources of sound S1 and S2 produce sound waves of same frequency 660 Hz. A listener is moving from source S1 towards S2 with a constant speed u m/s and he hears 10 beats/s. The velocity of sound is 330 m/s. Then, u equals :
Options:
A) 10.0 m/s
B) 5.5 m/s
C) 15.0 m/s
D) 2.5 m/s
172
MediumJEE Mains2019
A tuning fork of frequency 480 Hz is used in an experiment for measuring speed of sound (v) in air by resonance tube method. Resonance is observed to occur at two successive lengths of the air column, l1 = 30 cm and l2 = 70 cm. Then, v is equal to -
Options:
A) 338 ms–1
B) 384 ms–1
C) 379 ms–1
D) 332 ms–1
173
MediumJEE Mains2019
A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 dB intensity sound ? [Given reference intensity of sound as 10–12 W/m2 ]
Options:
A) 20 cm
B) 10 cm
C) 40 cm
D) 30 cm
174
MediumJEE Mains2019
A progressive wave travelling along the positive x-direction is represented by y(x,t) = Asin(kx – $\omega t + \phi ). Its snapshot at t = 0 is given in the figure. For this wave, the phase \phi $ is :
Options:
A) {\pi \over 2}
B) \pi
C) 0
D) - {\pi \over 2}
175
MediumJEE Mains2019
A submarine (A) travelling at 18 km/hr is being chased along the line of its velocity by another submarine (B) travelling at 27 km/hr. B sends a sonar signal of 500 Hz to detect A and receives a reflected sound of frequency $\upsilon . The value of \upsilon $ is close to: (Speed of sound in water =1500 ms–1)
Options:
A) 507 Hz
B) 502 Hz
C) 499 Hz
D) 504 Hz
176
MediumJEE Mains2019
The correct figure that shows, schematically, the wave pattern produced by superposition of two waves of frequencies 9 Hz and 11 Hz, is :
Options:
A)
B)
C)
D)
177
MediumJEE Mains2019
A source of sound S is moving with a velocity of 50 m/s towards a stationary observer. The observer measures the frequency of the source as 1000 Hz. What will be the apparent frequency of the source when it is moving away from the observer after crossing him? (Take velocity of sound in air is 350 m/s)
Options:
A) 750 Hz
B) 857 Hz
C) 807 Hz
D) 1143 Hz
178
MediumJEE Mains2019
A stationary source emits sound waves of frequency 500 Hz. Two observers moving along a line passing through the source detect sound to be of frequencies 480 Hz and 530 Hz. Their respective speeds are, in ms–1, (Given speed of sound = 300 m/s)
Options:
A) 12, 18
B) 16, 14
C) 12, 16
D) 8, 18
179
MediumJEE Mains2019
A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is :-
Options:
A) 180m/s, 80 Hz
B) 180m/s, 120 Hz
C) 320m/s, 120 Hz
D) 320m/s, 80 Hz
180
MediumJEE Mains2019
Two cars A and B are moving away from each other in opposite directions. Both the cars are moving with a speed of 20 ms–1 with respect to the ground. If an observer in car A detects a frequency 2000 Hz of the sound coming from car B, what is the natural frequency of the sound source in car B ? (speed of sound in air = 340 ms–1) :-
Options:
A) 2300 Hz
B) 2060 Hz
C) 2250 Hz
D) 2150 Hz
181
MediumJEE Mains2019
A string is clamped at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is Y = 0.3 sin(0.157x) cos(200pt). The length of the string is : (All quantities are in SI units.)
Options:
A) 60 m
B) 20 m
C) 80 m
D) 40 m
182
MediumJEE Mains2019
The pressure wave, P = 0.01 sin [1000t – 3x] Nm–2, corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is 0°C. On some other day, when temperature is T, the speed of sound produced by the same blade and at the same frequency is found to be 336 ms–1 . Approximate value of T is
Options:
A) 12°C
B) 15°C
C) 4°C
D) 11°C
183
MediumJEE Mains2019
A wire of length 2L, is made by joining two wires A and B of same length but different radii r and 2r and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire A is p and that in B is q then the ratio p : q is :
Options:
A) 3 : 5
B) 4 : 9
C) 1 : 2
D) 1 : 4
184
MediumJEE Mains2019
A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled with water to a mark 11 cm below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency 256 Hz which produces first resonance when water reaches a mark 27 cm below the reference mark. The velocity of sound in air, obtained in the experiment, is close to :
Options:
A) 335 ms–1
B) 328 ms–1
C) 341 ms–1
D) 322 ms–1
185
MediumJEE Mains2019
A travelling harmonic wave is represented by the equation y(x,t) = 10–3sin (50t + 2x), where, x and y are in mater and t is in seconds. Which of the following is a correct statement about the wave ?
Options:
A) The wave is propagating along the positive x-axis with speed 100 ms–1
B) The wave is propagating along the positive x-axis with speed 25 ms–1
C) The wave is propagating along the negative x-axis with speed 25 ms–1
D) The wave is propagating along the negative x-axis with speed 100 ms–1
186
MediumJEE Mains2019
Equation of travelling wave on a stretched string of linear density 5 g/m is y = 0.03 sin(450 t – 9x) where distance and time are measured in SI units. The tension in the string is :
Options:
A) 10 N
B) 7.5 N
C) 5 N
D) 12.5 N
187
MediumJEE Mains2019
A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The string is set into vibration using an external vibrator of frequency 100 Hz. The separation between successive nodes on the string is close to -
Options:
A) 16.6 cm
B) 10.0 cm
C) 20.0 cm
D) 33.3 cm
188
MediumJEE Mains2019
A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered by the observer is ƒ1. If the speed of the train is reduced to 17 m/s, the frequency registered is ƒ2. If speed of sound is 340 m/s, then the ratio ƒ1/ƒ2 is -
Options:
A) 19/18
B) 20/19
C) 21/20
D) 18/17
189
MediumJEE Mains2019
A musician using an open flute of length 50 cm producess second harmonic sound waves. A person runs towards the musician from another end of hall at a speed of 10 km/h. If the wave speed is 330 m/s, the frequency heard by the running person shall be close to :
Options:
A) 666 Hz
B) 753 Hz
C) 500 Hz
D) 333 Hz
190
MediumJEE Mains2019
A heavy ball of mass M is suspendeed from the ceiling of a car by a light string of mass m (m < < M). When the car is at rest, the speed of transverse waves in the string is 60 ms$-1. When the car has acceleration a, the wave-speed increases to 60.5 ms-$1. The value of a, in terms of gravitational acceleration g, is closest to :
Options:
A) {g \over {30}}
B) {g \over 5}
C) {g \over 10}
D) {g \over 20}
191
MediumJEE Mains2018
Two sitar strings, A and B, playing the note 'Dha' are slightly out of tune and produce beats of frequency 5 Hz. The tension of the string B s slightly increased and the beat frequency is found to decrease by 3Hz. If the frequency of A is 425 Hz, the original frequency of B is :
Options:
A) 430 Hz
B) 420 Hz
C) 428 Hz
D) 422 Hz
192
MediumJEE Mains2018
The end correction of a resonance column is 1 cm. If the shortest length resonating with the tunning fork is 10 cm, the next resonating length should be :
Options:
A) 28 cm
B) 32 cm
C) 36 cm
D) 40 c
193
MediumJEE Mains2018
A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7 $\times 103 kg/m3 and its Young’s modulus is 9.27 \times$ 1010 Pa. What will be the fundamental frequency of the longitudinal vibrations ?
Options:
A) 7.5 kHz
B) 5 kHz
C) 2.5 kHz
D) 10 kHz
194
MediumJEE Mains2018
5 beats / econd are heard when a tuning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either 0.95 m or 1 m. The frequency of the fork will be :
Options:
A) 195 Hz
B) 150 Hz
C) 300 Hz
D) 251 Hz
195
MediumJEE Mains2018
A tuning fork vibrates with frequency $256 Hz and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe ? (Speed of sound in air is 340\,m{s^{ - 1}}$)
Options:
A) 220 cm
B) 190 cm
C) 180 cm
D) 200 cm
196
MediumJEE Mains2017
A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by y(x, t) = 0.5 sin $\left( {{{5\pi } \over 4}x} \right)\, cos(200 \pi $t). What is the speed of the travelling wave moving in the positive x direction ? (x and t are in meter and second, respectively.)
Options:
A) 160 m/s
B) 90 m/s
C) 180 m/s
D) 120 m/s
197
MediumJEE Mains2017
In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r1 and r2 . The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be 5×10−4 s, the difference in radii, $\left| {} \right.r1 - r2 \left| {} \right.$ is best given by :
Options:
A) 1 cm
B) 0.05 cm
C) 0.5 cm
D) 0.01 cm
198
MediumJEE Mains2017
Two wires W1 and W2 have the same radius r and respective densities $\rho 1 and \rho 2 such that ρ2 = 4\rho $1 . They are joined together at the point O, as shown in the figure. The combination is used as a sonometer wire and kept under tension T. The point O is midway between the two bridges. When a stationary wave is set up in the composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in W1 to W2 is :
Options:
A) 1 : 1
B) 1 : 2
C) 1 : 3
D) 4 : 1
199
MediumJEE Mains2017
An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz. What is the frequency of the microwave measured by the observer? (speed of light = 3 ×108 ms–1)
Options:
A) 15.3 GHz
B) 10.1 GHz
C) 12.1 GHz
D) 17.3 GHz
200
MediumJEE Mains2016
A toy-car, blowing its horn, is moving with a steady speed of 5 m/s, away from a wall. An observer, towards whom the toy car is moving, is able to hear 5 beats per second. If the velocity of sound in air is 340 m/s, the frequency of the horn of the toy car is close to :
Options:
A) 680 Hz
B) 510 Hz
C) 340 Hz
D) 170 Hz
201
MediumJEE Mains2016
Two engines pass each other moving in opposite directions with uniform speed of 30 m/s. One of them is blowing a whistle of frequency 540 Hz. Calculate the frequency heard by driver of second engine before they pass each other. Speed of sound is 330 m/sec :
Options:
A) 450 Hz
B) 540 Hz
C) 648 Hz
D) 270 Hz
202
MediumJEE Mains2016
A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now :
Options:
A) 2f
B) f
C) {f \over 2}
D) {3f \over 4}
203
MediumJEE Mains2016
A uniform string of length $20 m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the supports is : (take {\,\,g = 10m{s^{ - 2}}}$ )
Options:
A) 2\sqrt 2 s
B) 2\pi \sqrt 2 s
C) 2\pi \sqrt 2 s
D) 2 s
204
MediumJEE Mains2015
A train is moving on a straight track with speed $20\,m{s^{ - 1}}. It is blowing its whistle at the frequency of 1000 Hz. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound = 320\,m{s^{ - 1}}$) close to :
Options:
A) 18\%
B) 24\%
C) 6\%
D) 12\%
205
MediumJEE Mains2014
A pipe of length $85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s$.
Options:
A) 12
B) 8
C) 6
D) 4
206
MediumJEE Mains2013
A sonometer wire of length $1.5 m is made of steel. The tension in it produces an elastic strain of 1\% . What is the fundamental frequency of steel if density and elasticity of steel are 7.7 \times {10^3}\,kg/{m^3} and 2.2 \times {10^{11}}\,N/{m^2}$ respectively ?
Options:
A) 188.5 Hz
B) 178.2 Hz
C) 200.5 Hz
D) 770 Hz
207
MediumJEE Mains2012
A cylindrical tube, open at both ends, has a fundamental frequency, $f,$ in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now :
Options:
A) f
B) f/2
C) 3/4
D) 2f
208
MediumJEE Mains2011
The transverse displacement $y(x, t) of a wave on a string is given by y\left( {x,t} \right) = {e^{ - \left( {a{x^2} + b{t^2} + 2\sqrt {ab} \,xt} \right)}}. This represents a:
Options:
A) wave moving in $-x direction with speed \sqrt {{b \over a}}
B) standing wave of frequency $\sqrt b
C) standing wave of frequency ${1 \over {\sqrt b }}
D) wave moving in $+x direction speed \sqrt {{a \over b}}
209
MediumJEE Mains2010
The equation of a wave on a string of linear mass density $0.04\,\,kg\,{m^{ - 1}} is given by y = 0.02\left( m \right)\,\sin \left[ {2\pi \left( {{t \over {0.04\left( s \right)}} - {x \over {0.50\left( m \right)}}} \right)} \right].$$ The tension in the string is
Options:
A) 4.0N
B) 12.5 N
C) 0.5 N
D) 6.25 N
210
MediumJEE Mains2009
Three sound waves of equal amplitudes have frequencies $\left( {v - 1} \right),\,v,\,\left( {v + 1} \right).$ They superpose to give beats. The number of beats produced per second will be :
Options:
A) 3
B) 2
C) 1
D) 4
211
MediumJEE Mains2009
A motor cycle starts from rest and accelerates along a straight path at $2m/{s^2}. At the starting point of the motor cycle there is a stationary electric siren. How far has the motor cycle gone when the driver hears the frequency of the siren at 94\% of its value when the motor cycle was at rest? (Speed of sound = 330\,m{s^{ - 1}}$)
Options:
A) 98 m
B) 147 m
C) 196\,m
D) 49 m
212
MediumJEE Mains2008
A wave travelling along the $x-axis is described by the equation y(x, t)=0.005 \cos \,\left( {\alpha \,x - \beta t} \right). If the wavelength and the time period of the wave are 0.08 m and 2.0s, respectively, then \alpha and \beta $ in appropriate units are
Options:
A) \alpha = 25.00\pi ,\,\beta = \pi
B) \alpha = {{0.08} \over \pi },\,\beta = {{2.0} \over \pi }
C) \alpha = {{0.04} \over \pi },\,\beta = {{1.0} \over \pi }
D) \alpha = 12.50\pi ,\,\beta = {\pi \over {2.0}}
213
MediumJEE Mains2008
While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of $18 cm during winter. Repeating the same experiment during summer, she measures the column length to be x cm$ for the second resonance. Then
Options:
A) 18 > x
B) x > 54
C) 54 > x > 36
D) 36 > x > 18
214
MediumJEE Mains2007
A sound absorber attenuates the sound level by $20 dB$. The intensity decreases by a factor of
Options:
A) 100
B) 1000
C) 10000
D) 10
215
MediumJEE Mains2006
A whistle producing sound waves of frequencies $9500 Hz and above is approaching a stationary person with speed v m{s^{ - 1}}. The velocity of sound in air is 300\,m{s^{ - 1}}. If the person can hear frequencies upto a maximum of 10,000 HZ, the maximum value of v$ upto which he can hear whistle is
Options:
A) 15\sqrt 2 \,\,m{s^{ - 1}}
B) {{15} \over {\sqrt 2 }}\,m{s^{ - 1}}
C) 15\,\,m{s^{ - 1}}
D) 30\,\,m{s^{ - 1}}
216
MediumJEE Mains2006
A string is stretched between fixed points separated by $75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz$. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is
Options:
A) 105 Hz
B) 1.05 Hz
C) 1050 Hz
D) 10.5 Hz
217
MediumJEE Mains2005
When two tuning forks (fork $1 and fork 2) are sounded simultaneously, 4 beats per second are heated. Now, some tape is attached on the prong of the fork 2. When the tuning forks are sounded again, 6 beats per second are heard. If the frequency of fork 1 is 200 Hz, then what was the original frequency of fork 2$ ?
Options:
A) 202 Hz
B) 200 Hz
C) 204 Hz
D) 196 Hz
218
MediumJEE Mains2005
An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency ?
Options:
A) 0.5\%
B) zero
C) 20\%
D) 5\%
219
MediumJEE Mains2004
The displacement $y of a particle in a medium can be expressed as, y = {10^{ - 6}}\,\sin \left( {100t + 20x + {\pi \over 4}} \right) m where t is in second and x$ in meter. The speed of the wave is
Options:
A) 20\,\,m/s
B) 5\,m/s
C) 2000\,m/s
D) 5\,\pi \,m/s
220
MediumJEE Mains2003
A metal wire of linear mass density of $9.8 g/m is stretched with a tension of 10 kg-wt between two rigid supports 1 metre apart. The wire passes at its middle point between the poles of a permanent magnet, and it vibrates in resonance when carrying an alternating current of frequency n. The frequency n$ of the alternating source is
Options:
A) 50 Hz
B) 100 Hz
C) 200 Hz
D) 25 Hz
221
MediumJEE Mains2003
The displacement $y of a wave travelling in the x-direction is given by y = {10^{ - 4}}\,\sin \left( {600t - 2x + {\pi \over 3}} \right)\,\,metres where x is expressed in metres and t in seconds. The speed of the wave - motion, in m{s^{ - 1}}$, is
Options:
A) 300
B) 600
C) 1200
D) 200
222
MediumJEE Mains2003
A tuning fork of known frequency $256 Hz makes 5 beats per second with the vibrating string of a piano. The beat frequency decreases to 2$ beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was
Options:
A) 256 + 2Hz
B) 256 - 2Hz
C) 256 - 5Hz
D) 256 + 5Hz
223
MediumJEE Mains2002
A tuning fork arrangement (pair) produces $4 beats/sec with one fork of frequency 288 cps. A little wax is placed on the unknown fork and it then produces 2$ beats/sec. The frequency of the unknown fork is
Options:
A) 286 cps
B) 292 cps
C) 294 cps
D) 288 cps
224
MediumJEE Mains2002
length of a string tied to two rigid supports is $40 cm. Maximum length (wavelength in cm$) of a stationary wave produced on it is
Options:
A) 20
B) 80
C) 40
D) 120
225
MediumJEE Mains2002
When temperature increases, the frequency of a tuning fork
Options:
A) increases
B) decreases
C) remains same
D) increases or decreases depending on the material
226
MediumJEE Mains2002
Tube $A has bolt ends open while tube B has one end closed, otherwise they are identical. The ratio of fundamental frequency of tube A and B$ is
Options:
A) 1:2
B) 1:4
C) 2:1
D) 4:1
227
MediumJEE Mains2002
A wave $y=a \sin \left( {\omega t - kx} \right) on a string meets with another wave producing a node at x=0.$ Then the equation of the unknown wave is
Options:
A) y = a\,\sin \,\left( {\omega t + kx} \right)
B) y = - a\,\sin \,\left( {\omega t + kx} \right)
C) y = a\,\sin \,\left( {\omega t - kx} \right)
D) y = - a\,\sin \,\left( {\omega t - kx} \right)
228
MediumMHT CET2025
A person observes two moving trains. First reaching the station and another leaves the station with equal speed of 30 \mathrm{~m} / \mathrm{s}. If both trains emit sounds of frequency 300 Hz , difference of frequencies heard by the person will be (speed of sound in air 330 \mathrm{~m} / \mathrm{s} )
Options:
A) 80 Hz
B) 75 Hz
C) 55 Hz
D) 45 Hz
229
MediumMHT CET2025
An open organ pipe and closed organ pipe of same length produce 2 beats per second, when they are set into vibrations together, in fundamental mode. The length of open pipe is made half and that of closed pipe is doubled. The number of beats produced per second will be (neglect end correction)
Options:
A) 4
B) 6
C) 7
D) 8
230
MediumMHT CET2025
An organ pipe closed at one end has fundamental frequency of 1500 Hz . The maximum number of overtones generated by this pipe which a normal person can hear is (Normal man can hear the frequency up to 19.5 kHz , Neglect end correction)
Options:
A) 6
B) 3
C) 13
D) 11
231
MediumMHT CET2025
The distance between two consecutive points with phase difference of 45^{\circ} in a wave of frequency 300 Hz is 4.0 m . The velocity of the travelling wave is (in \mathrm{km} / \mathrm{s} )
Options:
A) 1.6
B) 3.6
C) 4.8
D) 9.6
232
MediumMHT CET2025
The fundamental frequency of an air column in a pipe closed at one end is 150 Hz . If the same pipe is open at both the end, the frequencies produced in Hz are
Options:
A) 150,300,450,600,........
B) 300,450,600,750,........
C) 300,400,500,600,........
D) 300,600,900,1200,........
233
MediumMHT CET2025
When the observer moves towards a stationary source with velocity \mathrm{V}_1, the apparent frequency of emitted note is F_1. When observer moves away from the source with velocity \mathrm{V}_1, the apparent frequency is \mathrm{F}_2. If V is the velocity of sound in air and F_1 / F_2=2 then V / V_1 is equal to
Options:
A) 3
B) 2
C) 1
D) 4
234
MediumMHT CET2025
A musical instrument ' P ' produce sound waves of frequency ' n ' and amplitude ' A '. Another musical instrument ' Q ' produces sound waves of frequency ' \frac{\mathrm{n}}{4} ' The waves produced by ' P ' and ' Q ' have equal energies. If the amplitude of waves produced by ' P ' is ' \mathrm{A}_{\mathrm{p}} ', the amplitude of waves produced by ' Q ' will be
Options:
A) 2 A_p
B) 4 A_p
C) 6 A_p
D) 9 A_p
235
MediumMHT CET2025
The closed and open organ pipes have same length. When they are vibrating simultaneously in first overtone, they produce four beats. The length of open pipe is made half and that of the closed pipe is made two times the original. Now the number of beats produced if the two pipes are vibrating in their fundamental modes simultaneously is
Options:
A) 8
B) 10
C) 14
D) 16
236
MediumMHT CET2025
Fundamental frequency of sonometer wire is ' n '. If the tension and length are increased 3 times and diameter is increased twice, the new frequency will be
Options:
A) 2 n
B) \frac{\sqrt{3}}{2} n
C) \frac{n}{2 \sqrt{3}}
D) \sqrt{3} n
237
MediumMHT CET2025
A source of sound emits sound wave of frequency ' f ' and moves towards an observer with a velocity \frac{\mathrm{V}}{3} where V is the velocity of sound. If the observer moves away from the source with a velocity \frac{\mathrm{V}}{5} the apparent frequency heard by him will be
Options:
A) \frac{15}{2} \mathrm{f}
B) \frac{8}{15} \mathrm{f}
C) \frac{6}{5} \mathrm{f}
D) \frac{15}{18} \mathrm{f}
238
MediumMHT CET2025
An air column is of length 17 cm . The ratio of frequencies of 5^{\text {th }} overtone if the air column is closed at one end to that open at both ends is (velocity of sound in air =340 \mathrm{~ms}^{-1} )
Options:
A) \frac{9}{11}
B) \frac{5}{7}
C) \frac{11}{12}
D) \frac{13}{9}
239
MediumMHT CET2025
In Sonometer experiment, the frequency of a tuning fork used is 288 Hz . Harmonics will 'NOT' be produced at the frequency
Options:
A) 288 Hz
B) 576 Hz
C) 844 Hz
D) 864 Hz
240
MediumMHT CET2025
The fundamental frequencies of vibrations of air column in pipe open at both ends and in pipe closed at one end are ' \mathrm{n}_1 ' and ' \mathrm{n}_2 ' respectively, then
Options:
A) \mathrm{n}_1=\mathrm{n}_2
B) \mathrm{n}_1=2 \mathrm{n}_2
C) \quad 2 n_1=n_2
D) 3 n_1=4 n_2
241
MediumMHT CET2025
In an open end organ pipe of length ' L ', if the velocity of sound is ' V ', then the fundamental frequency will be (Neglect end correction)
Options:
A) \frac{\mathrm{V}}{2 \mathrm{~L}} and all harmonics are present.
B) \frac{\mathrm{V}}{4 \mathrm{~L}} and all harmonics are present.
C) \frac{\mathrm{V}}{2 \mathrm{~L}} and even harmonics are present.
D) \frac{\mathrm{V}}{4 \mathrm{~L}} and even harmonics are present.
242
MediumMHT CET2025
At what speed should a source of sound move so that the observer finds the apparent frequency equal to half the original frequency?
Options:
A) \frac{\mathrm{V}}{2}
B) 2 V
C) \frac{\mathrm{V}}{4}
D) V
243
MediumMHT CET2025
A tuning fork gives 5 beats per second with 40 cm length of sonometer wire. If the length of the wire is shortened by 1 cm , the number of beats is still the same. The frequency of the fork is
Options:
A) 390 Hz
B) 395 Hz
C) 400 Hz
D) 405 Hz
244
MediumMHT CET2025
A sound source is moving towards a stationary observer with \left(\frac{1}{10}\right)^{\text {th }} the speed of sound, The ratio of apparent to real frequency is
Options:
A) \frac{10}{9}
B) \frac{11}{10}
C) \left(\frac{11}{10}\right)^2
D) \left(\frac{9}{10}\right)^2
245
MediumMHT CET2025
The fundamental frequency of a closed pipe is 400 Hz . If \left(\frac{1}{3}\right)^{\text {rd }} length of the pipe is filled with water, the frequency of the 2^{\text {nd }} harmonic of the pipe will be (Neglect end correction)
Options:
A) 1500 Hz
B) 1200 Hz
C) 600 Hz
D) 1800 Hz
246
MediumMHT CET2025
At poles, a stretched wire of a given length vibrates in unison with a tuning fork. At the equator, for same setting, to produce resonance with same fork, the vibrating length of wire
Options:
A) should be decreased.
B) should be increased.
C) should be same.
D) should be three times.
247
MediumMHT CET2025
Two tuning forks of frequencies 256 Hz and 258 Hz are sounded together. The time interval between two consecutive maxima is
Options:
A) 250 s
B) 252 s
C) 2 s
D) 0.5 s
248
MediumMHT CET2025
If a source emitting waves of frequency ' F ' moves towards an observer with a velocity \frac{\mathrm{V}}{3} and the observer moves away from the source with a velocity \frac{\mathrm{V}}{4}, the apparent frequency as heard by the observer will be ( \mathrm{V}= velocity of sound)
Options:
A) \frac{9}{8} \mathrm{~F}
B) \frac{8}{9} \mathrm{~F}
C) \frac{3}{4} \mathrm{~F}
D) \frac{4}{3} \mathrm{~F}
249
MediumMHT CET2025
Two sound waves travelling in the same direction have displacement \mathrm{y}_1=\mathrm{a} \sin (0.2 \pi \mathrm{x}-50 \pi \mathrm{t}) and \mathrm{y}_2=\mathrm{a} \sin (0.15 \pi \mathrm{x}-46 \pi \mathrm{t}). How many times, a listener can hear sound of maximum intensity in one second?
Options:
A) 1
B) 2
C) 3
D) 4
250
MediumMHT CET2025
An open organ pipe is closed such that the third overtone of the closed pipe is found to be higher in frequency by 200 Hz than the second overtone of the original pipe. The fundamental frequency of the open pipe is (Neglect end correction)
Options:
A) 150 Hz
B) 200 Hz
C) 400 Hz
D) 500 Hz
251
MediumMHT CET2025
The fundamental frequency of sonometer wire is ' n '. If the tension and length are increased 3 times and diameter is increased twice, the new frequency will be
Options:
A) \sqrt{\frac{3}{2}} \mathrm{n}
B) \frac{\sqrt{3}}{2} n
C) \frac{n}{2 \sqrt{3}}
D) 2 \sqrt{3} n
252
MediumMHT CET2025
A particle performs S.H.M. of amplitude 'A' and wavelength ' \lambda ', Then the velocity of the wave (V) and the maximum particle velocity (v) are related as
Options:
A) v=\frac{\lambda V}{4 \pi A}
B) \quad V=\frac{\lambda v}{4 \pi A}
C) \quad v=\frac{2 \pi A}{\lambda} v
D) V=\frac{2 \pi A}{\lambda} v
253
MediumMHT CET2025
Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneously with tensions ' \mathrm{T}_1 ' and ' \mathrm{T}_2 ' respectively. On changing the tension slightly in one of them, the beat frequency remains unchanged. This will happen when (Given \rightarrow \mathrm{T}_1>\mathrm{T}_2 )
Options:
A) \mathrm{T}_1 is increased or \mathrm{T}_2 is decreased
B) \mathrm{T}_1 is increased by 144
C) \mathrm{T}_2 is decreased by 144
D) T_1 is decreased or T_2 is increased
254
MediumMHT CET2025
An observer moves towards a stationary source of sound with a velocity of one fifth of the velocity of sound. The percentage increase in the apparent frequency is
Options:
A) 5 \%
B) 10 \%
C) 20 \%
D) 25 \%
255
MediumMHT CET2025
Two tuning forks when sounded together produce 4 beats per second. One of the forks is in unison with 23 cm length of sonometer wire and other with 24 cm length of the same wire. The frequencies of the two tuning forks are
Options:
A) 96 \mathrm{~Hz}, 92 \mathrm{~Hz}
B) 92 \mathrm{~Hz}, 88 \mathrm{~Hz}
C) 72 \mathrm{~Hz}, 68 \mathrm{~Hz}
D) 48 \mathrm{~Hz}, 44 \mathrm{~Hz}
256
MediumMHT CET2025
A pipe open at both ends produces a fundamental frequency n_1. When the pipe is kept with \frac{3^{\text {th }}}{4} of its length in water, it produces a note of fundamental frequency \mathrm{n}_2. The ratio of \frac{\mathrm{n}_1}{\mathrm{n}_2} is
Options:
A) \frac{4}{3}
B) \frac{3}{4}
C) 2
D) \frac{1}{2}
257
MediumMHT CET2025
In a pipe closed at one end, air column is vibrating in its second overtone. The column has
Options:
A) three nodes and three antinodes.
B) three nodes and four antinodes.
C) two nodes and three antinodes.
D) four nodes and three antinodes.
258
MediumMHT CET2025
The fundamental frequency of a sonometer wire is 50 Hz for some length and tension. If the length is increased by 25 \% by keeping tension same then frequency change of second harmonic is
Options:
A) increased by 20 \%
B) decreased by 20 \%
C) increased by 10 \%
D) decreased by 10 \%
259
MediumMHT CET2025
When source of sound and observer both are moving towards each other, the observer will hear
Options:
A) low frequency, low wavelength.
B) low frequency, high wavelength.
C) high frequency, low wavelength.
D) high frequency, high wavelength.
260
MediumMHT CET2025
The lengths of the two organ pipes open at both ends are ' L ' and \left(\mathrm{L}+\mathrm{L}_1\right). If they are sounded together, the beat frequency will be ( \mathrm{v}= velocity of sound in air)
Options:
A) \frac{2 v L_1}{L\left(L+L_1\right)}
B) \frac{2 \mathrm{~L}\left(\mathrm{~L}+\mathrm{L}_1\right)}{\mathrm{vL}_1}
C) \frac{\mathrm{vL}_1}{\mathrm{~L}\left(\mathrm{~L}+\mathrm{L}_1\right)}
D) \frac{v L_1}{2 L\left(L+L_1\right)}
261
MediumMHT CET2025
A person standing between two parallel cliffs fires a gun and hears two echoes, first echo after 1 second and the second echo after 3 second. The distance between the two cliffs is (Velocity of sound =340 \mathrm{~m} / \mathrm{s} )
Options:
A) 340 m
B) 680 m
C) 1020 m
D) 1360 m
262
MediumMHT CET2025
An organ pipe has fundamental frequency 80 Hz . If its one end is closed, the frequencies produced will be (in Hz ) (Neglect end correction)
Options:
A) 40,80,120,160
B) 40,80,160,240
C) 40,120,200,280
D) 80,160,240,320
263
MediumMHT CET2025
The equation of wave is y=60 \sin (1200 t-6 x), where ' y ' is in micron, ' t ' is in second and ' x ' is in metre. The ratio of maximum particle velocity to the wave velocity of wave propagation is
Options:
A) 36
B) 3.6 \times 10^{-5}
C) 3.6 \times 10^{-4}
D) 3.6 \times 10^{-6}
264
MediumMHT CET2025
Two waves of same frequency ( n ) are approaching each other with same velocity 12 \mathrm{~m} / \mathrm{s} along the same linear path and interfere. The distance between two consecutive nodes is
Options:
A) 12 n
B) \frac{12}{n}
C) 6 n
D) \frac{6}{n}
265
MediumMHT CET2025
Two strings ' X ' and ' Y ' of a guitar produces a beat frequency of 6 Hz . When the tension of the string ' Y ' is increased, the beat frequency is found to be 4 Hz . If the frequency of string ' X ' is 300 Hz , then the original frequency of string ' Y ' is
Options:
A) 296 Hz
B) 294 Hz
C) 306 Hz
D) 304 Hz
266
MediumMHT CET2025
A transverse displacement of vibrating string is y=0.06 \sin \left(\frac{2 \pi}{3}\right) \times \cos (120 \pi t). If the mass per unit length of a string is 4 \times 10^{-2} \mathrm{~kg} / \mathrm{m}, then the tension in the string will be
Options:
A) 1296 N
B) 1000 N
C) 720 N
D) 500 N
267
MediumMHT CET2025
The equation of a progressive wave is \mathrm{Y}=3 \sin \left[\pi\left(\frac{\mathrm{t}}{3}-\frac{\mathrm{x}}{5}\right)+\frac{\pi}{4}\right] where x and y are in meter and time in second. Which of the following is correct?
Options:
A) Wavelength =10 \mathrm{~m}
B) Velocity =1.5 \mathrm{~m} / \mathrm{s}
C) Amplitude =3 \mathrm{~cm}
D) Frequency =0.2 \mathrm{~Hz}
268
MediumMHT CET2025
A vehicle starts from rest and accelerates along straight path at 2 \mathrm{~m} / \mathrm{s}^2. At the starting point of the vehicle, there is a stationary electric siren. How far has the vehicle nearly gone when the driver hears the siren at 94 \% of its value when the vehicle was at rest? (speed of sound =220 \mathrm{~m} / \mathrm{s} )
Options:
A) 98 m
B) 49 m
C) 196 m
D) 24.5 m
269
MediumMHT CET2025
A pipe open at both ends of length 1.5 m is dipped in water at one end such that 2^{\text {nd }} overtone of vibrating air column is resonating with a tuning fork of frequency 330 Hz . The length of the pipe immersed in water is (Speed of sound in air =330 \mathrm{~m} / \mathrm{s} ) (Neglect end correction)
Options:
A) 1 m
B) 0.75 m
C) 0.5 m
D) 0.25 m
270
MediumMHT CET2025
Two uniform wires of same material are vibrating under the same tension. If the 1^{\text {st }} overtone of 1^{\text {st }} wire is equal to the 2^{\text {nd }} overtone of 2^{\text {nd }} wire and radius of 1^{\text {st }} wire is twice the radius of 2^{\text {nd }} wire, the ratio of length of 1^{\text {st }} wire to that 2^{\text {nd }} wire is
Options:
A) 1: 3
B) 3: 1
C) 2: 3
D) 3: 5
271
MediumMHT CET2025
An observer on sea-coast counts 45 waves in one minute. If the wavelength of the waves is 7 m , then the velocity of the waves will be
Options:
A) 4.75 \mathrm{~m} / \mathrm{s}
B) 5.25 \mathrm{~m} / \mathrm{s}
C) 7.5 \mathrm{~m} / \mathrm{s}
D) 8.65 \mathrm{~m} / \mathrm{s}
272
MediumMHT CET2025
Two sources of sound are emitting progressive waves \mathrm{y}_1=4 \sin 710 \pi \mathrm{t} and \mathrm{y}_2=3 \sin 702 \pi \mathrm{t}. The sources are placed close to each other. The number of beats heard per second and intensity ratio between waxing and waning are respectively
Options:
A) 4,16: 9
B) 8,16: 9
C) 4,49: 1
D) 8,49: 1
273
MediumMHT CET2025
The closed and open organ pipe have same length and when they are vibrating simultaneously in first overtone produce 3 beats. The length of open pipe is made \left(\frac{1}{3}\right)^{\mathrm{rd}} and that of closed pipe is made 3 times the original, the number of beats produced will be (Neglect end correction)
Options:
A) 14
B) 17
C) 18
D) 12
274
MediumMHT CET2025
The length of closed and open pipe is same. The ratio of frequency of \mathrm{n}^{\text {th }} overtone for closed pipe to that of open pipe is (Neglect end correction)
Options:
A) \frac{(2 n+1)}{2(n+1)}
B) \frac{(\mathrm{n}+1)}{(2 \mathrm{n}+1)}
C) \quad \frac{(2 n-1)}{2(n+1)}
D) \frac{(n-1)}{2(n+1)}
275
MediumMHT CET2025
The frequency of a stretched uniform wire of length L under tension is in resonance with the fundamental frequency of a closed pipe of same length. If the tension in the wire is increased by 8 N , it is in resonance with the first overtone of the same closed pipe. The initial tension in the wire is
Options:
A) 4 N
B) \quad \frac{1}{2} \mathrm{~N}
C) 2 N
D) 1 N
276
MediumMHT CET2025
When an observer moves towards a stationary source with velocity ' \mathrm{V}_1 ', the apparent frequency of emitted note is ' \mathrm{F}_1 '. When observer moves away from stationary source with velocity ' \mathrm{V}_1 ' the apparent frequency is ' \mathrm{F}_2 '. If ' v ' is velocity of sound in air and \frac{\mathrm{F}_1}{\mathrm{~F}_2}=2, then \frac{\mathrm{V}}{\mathrm{V}_1} is equal to
Options:
A) 6
B) 5
C) 3
D) 4
277
MediumMHT CET2025
In fundamental mode, the time required for the sound wave to reach up to closed end of a pipe filled with air is ' t ' second. The frequency of vibration of air column is (Neglect end correction)
Options:
A) (4 t)^{-1}
B) (2 t)^{-1}
C) 4 t
D) 2 t
278
MediumMHT CET2025
Two pipes of lengths \mathrm{L}_1 and \mathrm{L}_2, open at both ends are joined in series. If ' f_1 ' and ' f_2 ' are the fundamental frequencies of two pipes, then the fundamental frequency of series combination will be (neglect end correction)
Options:
A) \frac{f_1 f_2}{f_1-f_2}
B) \mathrm{f}_1+\mathrm{f}_2
C) \frac{f_1 f_2}{f_1+f_2}
D) \sqrt{\mathrm{f}_1^2+\mathrm{f}_2^2}
279
MediumMHT CET2025
A wire of length L , diameter ' d ' density of material ' e ' is under tension ' T ', having fundamental frequency of vibration \mathrm{n}_{\mathrm{A}}. Another wire of length 2 L , tension 2 T , density 2 e and diameter 3 d has fundamental frequency of vibration \mathrm{n}_{\mathrm{B}}. The ratio \mathrm{n}_{\mathrm{B}}: \mathrm{n}_{\mathrm{A}} is
Options:
A) 1: 2
B) 1: 4
C) 1: 6
D) 1: 8
280
MediumMHT CET2025
The frequency of a tuning fork is 256 Hz . It will not resonate with the tuning fork of frequency
Options:
A) 256 Hz
B) 512 Hz
C) 754 Hz
D) 768 Hz
281
MediumMHT CET2025
In an organ pipe closed at one end; the sum of the frequencies of first three overtones is 3930 Hz . The frequency of the fundamental mode of organ pipe is
Options:
A) 256 Hz
B) 262 Hz
C) 320 Hz
D) 384 Hz
282
MediumMHT CET2025
A progressive wave of frequency 400 Hz is travelling with velocity 336 \mathrm{~m} / \mathrm{s}. How far apart are the two points on a wave which are 60^{\circ} out of phase?
Options:
A) 0.12 m
B) 0.14 m
C) 0.21 m
D) 0.28 m
283
MediumMHT CET2025
When two tuning forks are sounded together, 6 beats per second are heard. One of the fork is in unison with 0.70 m length of sonometer wire and another fork is in unison with 0.69 m length of the same sonometer wire. The frequencies of the two tuning forks are
Options:
A) 320 \mathrm{~Hz}, 326 \mathrm{~Hz}
B) 414 \mathrm{~Hz}, 420 \mathrm{~Hz}
C) 420 \mathrm{~Hz}, 426 \mathrm{~Hz}
D) 480 \mathrm{~Hz}, 486 \mathrm{~Hz}
284
MediumMHT CET2025
When source of sound moves towards a stationary observer, the apparent frequency heard by him
Options:
A) increases and wavelength also increases.
B) increases while wavelength decreases.
C) remains the same while wavelength decreases.
D) decreases and wavelength remains the same.
285
MediumMHT CET2025
The frequency of fourth overtone of a closed pipe is in unison with the fifth overtone of an open pipe. The ratio of length of closed pipe to that of open pipe is
Options:
A) 2: 3
B) 3: 4
C) 4: 5
D) 5: 6
286
MediumMHT CET2025
A string of mass 0.1 \mathrm{kgm}^{-1} has length 0.9 m . It is fixed at both ends and stretched such that it has a tension of 40 N . The string vibrates in three segments with amplitude 0.3 cm . The amplitude (maximum) of the particle velocity is (in \mathrm{m} / \mathrm{s})
Options:
A) \frac{\pi}{2}
B) \frac{\pi}{3}
C) \frac{\pi}{5}
D) \frac{\pi}{6}
287
MediumMHT CET2025
The fundamental frequency of a closed pipe of length L is equal to the second overtone of a pipe open at both the ends of length (XL). The value of X is (Neglect end correction)
Options:
A) 4
B) 5
C) 6
D) 7
288
MediumMHT CET2024
Two sound waves having frequencies 250 Hz and 256 Hz superimpose to produce beat wave. The resultant beat wave has intensity maximum at \mathrm{t}=0. After how much time an intensity will be minimum produced at the same point?
Options:
A) \frac{1}{6} \mathrm{~s}
B) \frac{1}{24} \mathrm{~s}
C) \frac{1}{18} \mathrm{~s}
D) \frac{1}{12} \mathrm{~s}
289
MediumMHT CET2024
A pipe 60 cm long and open at both the ends produces harmonics. Which harmonic mode of pipe resonates a 2.2 KHz source? (Speed of sound in air =330 \mathrm{~m} / \mathrm{s})( Neglect end correction)
Options:
A) First
B) Eighth
C) Third
D) Second
290
MediumMHT CET2024
A source and listener are both moving towards each other with speed \frac{\mathrm{V}}{10}. (where V is speed of sound) If the frequency of sound note emitted by the source is ' n ', then the frequency heard by the listener would be nearly
Options:
A) 1.1 n
B) 1.22 n
C) n
D) 1.27 n
291
MediumMHT CET2024
Two uniform strings A and B made of steel are made to vibrate under the same tension. If first overtone of A is equal to the second overtone of B and if the radius of A is twice that of B, the ratio of the length of string B to that of A is
Options:
A) 1: 2
B) 4: 3
C) 2: 3
D) 3: 1
292
MediumMHT CET2024
A string is under tension of 180 N and mass per unit length 2 \times 10^{-3} \mathrm{Kg} / \mathrm{m}. It produces two consecutive resonant frequencies with a tuning fork, which are 375 Hz and 450 Hz . The mass of the string is
Options:
A) 1 gram
B) 2 gram
C) 3 gram
D) 4 gram
293
MediumMHT CET2024
How many times more intense is a 60 dB sound that a 30 dB sound?
Options:
A) 2
B) 4
C) 1000
D) 10000
294
MediumMHT CET2024
The end correction for the vibrations of air column in a tube of circular cross-section will be more if the tube is
Options:
A) reduced in length.
B) increased in length.
C) made thinner.
D) widened.
295
MediumMHT CET2024
A wave is given by Y=3 \sin 2 \pi\left(\frac{t}{0.04}-\frac{x}{0.01}\right) where Y is in cm . Frequency of the wave and maximum acceleration will be \left(\pi^2=10\right)
Options:
A) 100 \mathrm{~Hz}, 4.7 \times 10^4 \mathrm{~cm} / \mathrm{s}^2
B) 50 \mathrm{~Hz}, 7.5 \times 10^3 \mathrm{~cm} / \mathrm{s}^2
C) 25 \mathrm{~Hz}, 4.7 \times 10^4 \mathrm{~cm} / \mathrm{s}^2
D) 25 \mathrm{~Hz}, 7.5 \times 10^4 \mathrm{~cm} / \mathrm{s}^2
296
MediumMHT CET2024
Velocity of sound waves in air is 330 \mathrm{~m} / \mathrm{s}. For a particular sound wave in air, path difference of 40 cm is equivalent to phase difference of 1.6 \pi. frequency of this wave is
Options:
A) 165 Hz
B) 150 Hz
C) 660 Hz
D) 330 Hz
297
MediumMHT CET2024
A string has mass per unit length of 10^{-6} \mathrm{~kg} / \mathrm{cm} The equation of simple harmonic wave produced in it is \mathrm{Y}=0.2 \sin (2 \mathrm{x}+80 \mathrm{t}) \mathrm{m}. The tension in the string is
Options:
A) 0.16 N
B) 0.0016 N
C) \quad 1.6 \mathrm{~N}
D) 16 N
298
MediumMHT CET2024
The driver of a car travelling with a speed ' V_1 ' \mathrm{m} / \mathrm{s} towards a wall sounds a siren of frequency ' n ' Hz. If the velocity of sound in air is \mathrm{V} \mathrm{m} / \mathrm{s}, then the frequency of sound reflected from the wall and as heard by the driver, in Hz , is
Options:
A) \left(\frac{\mathrm{V}+\mathrm{V}_1}{\mathrm{~V}-\mathrm{V}_1}\right) \mathrm{n}
B) \left(\frac{V-V_1}{V+V_1}\right) n
C) \left(\frac{V_1-V}{V_1+V}\right) n
D) \left(\frac{V_1}{V_1-V}\right) n
299
MediumMHT CET2024
An open organ pipe of length ' l ' is sounded together with another open organ pipe of length \left(l+l_1\right) in their fundamental modes. Speed of sound in air is ' V '. The beat frequency heard will be ( \left.l_1< < l\right)
Options:
A) \frac{\mathrm{V} l_1^2}{2 l}
B) \frac{\mathrm{V} l_1}{2 l^2}
C) \frac{\mathrm{V} l_1}{4 l^2}
D) \frac{\mathrm{v} l^2}{2 l_1}
300
MediumMHT CET2024
Two progressive waves Y_1=\sin 2 \pi\left(\frac{t}{0 \cdot 4}-\frac{x}{4}\right) and Y_2=\sin 2 \pi\left(\frac{t}{0 \cdot 4}+\frac{x}{4}\right) superpose to form a standing wave. ' x ' and ' y ' are in SI system. Amplitude of the particle at x=0.5 \mathrm{~m} is \left[\sin 45^{\circ}=\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right]
Options:
A) \sqrt{3} \mathrm{~m}
B) 3 \sqrt{3} \mathrm{~m}
C) \sqrt{2} \mathrm{~m}
D) 2 \sqrt{2} \mathrm{~m}
301
MediumMHT CET2024
When a sonometer wire vibrates in third overtone there are
Options:
A) 4 nodes and 3 antinodes.
B) 6 nodes and 5 antinodes.
C) 5 nodes and 4 antinodes.
D) 4 nodes and 5 antinodes.
302
MediumMHT CET2024
Which of the following statements is NOT true?
Options:
A) Sound wave travels in a straight line.
B) Sound is propagated as waves.
C) Sound can travel through vacuum.
D) Sound is a form of energy.
303
MediumMHT CET2024
If the two waves of same amplitude, having frequencies 340 Hz and 335 Hz , are moving in same direction, then the time interval between two successive maxima formed (in second) is
Options:
A) 0.1
B) 0.2
C) 0.3
D) 0.5
304
MediumMHT CET2024
The frequency of the third overtone of a pipe of length ' L_{\mathrm{c}} ', closed at one end is same as the frequency of the sixth overtone of a pipe of length ' L_0 ', open at both ends. Then the ratio \mathrm{L}_{\mathrm{c}}: \mathrm{L}_0 is
Options:
A) 1: 4
B) 1: 2
C) 2: 1
D) 4: 1
305
MediumMHT CET2024
A wire of length ' L ' and linear density ' m ' is stretched between two rigid supports with tension ' T '. It is observed that wire resonates in the \mathrm{P}^{\text {th }} harmonic at a frequency of 320 Hz and resonates again at next higher frequency of 400 Hz . The value of ' p ' is
Options:
A) 2
B) 4
C) 8
D) 10
306
MediumMHT CET2024
The frequency of two tuning forks A and B are respectively 1.4 \% more and 2.6 \% less than that of the tuning fork C . When A and B are sounded together, 10 beats are produced in 1 second. The frequency of tuning fork C is
Options:
A) 250 Hz
B) 300 Hz
C) 340 Hz
D) 400 Hz
307
MediumMHT CET2024
A resonance tube closed at one end is of height 1.5 m . A tuning fork of frequency 340 Hz is vibrating above the tube. Water is poured in the tube gradually. The minimum height of water column for which resonance is obtained is (Neglect end correction, speed of sound in air =340 \mathrm{~m} / \mathrm{s} )
Options:
A) 75 cm
B) 50 cm
C) 30 cm
D) 25 cm
308
MediumMHT CET2024
At the poles of earth, a stretched wire of a given length vibrates in unison with a tuning fork. At the equator of earth, for same setting, to produce resonance with same fork, the vibrating length of wire
Options:
A) should be decreased.
B) should be increased.
C) should be same.
D) should be three times the original.
309
MediumMHT CET2024
With what velocity an observer should move relative to a stationary source so that a sound of triple the frequency of source is heard by an observer?
Options:
A) Same as velocity of sound towards the source.
B) Same as velocity of sound away from the source.
C) Half the velocity of sound towards the source.
D) Twice the velocity of sound towards the source.
310
MediumMHT CET2024
The length of a sonometer wire 'AB' is 110 cm . Where should the two bridges be placed from end ' A ' to divide the wire in three segments whose fundamental frequencies are in the ratio 1: 2: 3 ?
Options:
A) 60 cm and 90 cm
B) 90 cm and 100 cm
C) 40 cm and 80 cm
D) 50 cm and 90 cm
311
MediumMHT CET2024
Prong of a vibrating tuning fork is in contact with water surface. It produces concentric circular waves on the surface of water. The distance between five consecutive crests is 0.8 m and the velocity of wave on the water surface is 56 \mathrm{~m} / \mathrm{s}. The frequency of tuning fork is
Options:
A) 256 Hz
B) 280 Hz
C) 341 Hz
D) 512 Hz
312
MediumMHT CET2024
The end correction for the vibrations of air column in a tube of circular cross-section will be more if the tube is
Options:
A) reduced in length.
B) increased in length.
C) made thinner.
D) widened.
313
MediumMHT CET2024
Stationary wave is produced along the stretched string of length 80 cm . The resonant frequencies of string are 90 \mathrm{~Hz}, 150 \mathrm{~Hz} and 210 Hz . The speed of transverse wave in the string is
Options:
A) 45 m/s
B) 75 m/s
C) 48 m/s
D) 80 m/s
314
MediumMHT CET2024
The pipe open at both ends and pipe closed at one end have same length and both are vibrating in fundamental mode. Air column vibrating in open pipe has resonance frequency n_1 and air column vibrating in closed pipe has resonance frequency \mathrm{n}_2, then
Options:
A) \mathrm{n}_1=2 \mathrm{n}_2
B) \mathrm{n}_1=\mathrm{n}_2
C) 2 \mathrm{n}_1=\mathrm{n}_2
D) 3 \mathrm{n}_1=4 \mathrm{n}_2
315
MediumMHT CET2024
Two sound waves having displacements x_1=2 \sin (1000 \pi t) and x_2=3 \sin (1006 \pi t), when interfere, produce
Options:
A) 5 beats/s with maximum intensity 25 units
B) 6 beats/s with maximum intensity 16 units
C) 3 beats/s with maximum intensity 25 units
D) 1 beats/s with maximum intensity 5 units
316
MediumMHT CET2024
When the listener moves towards stationary source with velocity ' \mathrm{V}_1 ', the apparent frequency of emitted note is ' F_1 '. When observer moves away from the source with velocity ' \mathrm{V}_1 ', apparent frequency is ' F_2 '. If V is the velocity of sound in air and \frac{F_1}{F_2}=2 then \frac{V}{V_1} is
Options:
A) ,2
B) 3
C) 4
D) 5
317
MediumMHT CET2024
When the string is stretched between two rigid supports, under certain tension and vibrated
Options:
A) antinodes at both ends and at least one node in between
B) Nodes at both ends and at least one antinode in between
C) Nodes at both ends and no antinode in between
D) antinodes at both ends and no node in between
318
MediumMHT CET2024
A musical instrument X produces sound waves of frequency n and amplitude A. Another musical instrument Y produces sound waves of frequency \frac{n}{3}. The waves produced by x and y have equal energies. The amplitude of waves produced by Y will be
Options:
A) 3A
B) 4A
C) 2A
D) A
319
MediumMHT CET2024
A stationary wave is formed having 3 nodes along the length of the string 90 cm . The wavelength of the wave is
Options:
A) 60 cm
B) 75 cm
C) 90 cm
D) 30 cm
320
MediumMHT CET2024
The diagram shows the propagation of a progressive wave. A, B, C, D, E are five points on this wave Which of the following points are in the same state of vibration?
Options:
A) A, B
B) B, C
C) B, D
D) E, B
321
MediumMHT CET2024
A string of mass 0.2 Kg is under a tension of 2.5 N . The length of the string is 2 m. A transverse wave starts from one end of the string. The time taken by the wave to reach the other end is
Options:
A) 0.2 s
B) 0.4 s
C) 0.6 s
D) 0.8 s
322
MediumMHT CET2024
A musical instrument ' P ' produces sound waves of frequency ' n ' and amplitude ' A '. Another musical instrument ' Q ' produces sound waves of frequency \frac{\mathrm{n}}{4}. The waves produced by ' P ' and ' Q ' have equal energies. If the amplitude of waves produced by ' P ' is ' A_P ', the amplitude of waves produced by ' Q ' will be
Options:
A) 2 \mathrm{~A}_{\mathrm{P}}
B) 4 \mathrm{~A}_{\mathrm{P}}
C) 6 \mathrm{~A}_{\mathrm{p}}
D) 9 \mathrm{~A}_{\mathrm{P}}
323
MediumMHT CET2024
A sonometer wire is in unison with a tuning fork of frequency ' n ' when it is stretched by a weight of specific gravity ' d '. When the weight is completely immersed in water, ' x ' beats are produced per second, then
Options:
A) \frac{\mathrm{n}}{\mathrm{n}-\mathrm{x}}=\frac{\mathrm{d}}{\mathrm{d}-1}
B) \frac{n}{n-x}=\sqrt{\frac{d}{d-1}}
C) \frac{\mathrm{n}-\mathrm{x}}{\mathrm{n}}=\frac{\mathrm{d}-1}{\mathrm{~d}}
D) \frac{\mathrm{n}-\mathrm{x}}{\mathrm{n}}=\sqrt{\frac{\mathrm{d}}{\mathrm{d}-1}}
324
MediumMHT CET2024
The equations of two waves are given as $\begin{aligned} & y_1=a \sin \left(\omega t+\phi_1\right) \\ & y_2=a \sin \left(\omega t+\phi_2\right) \end{aligned} If amplitude and time period of resultant wave is same as the individual waves, then \left(\phi_1-\phi_2\right)$ is
Options:
A) \cos ^{-1}\left(\frac{-1}{2}\right)
B) \cos ^{-1}\left(\frac{-1}{4}\right)
C) \cos ^{-1}\left(-\frac{1}{6}\right)
D) \cos ^{-1}\left(-\frac{1}{8}\right)
325
MediumMHT CET2024
Two sound waves having same amplitude ' A ' and angular frequency ' \omega ' but having a phase difference of \left(\frac{\pi}{2}\right)^c are superimposed then the maximum amplitude of the resultant wave is
Options:
A) \frac{\mathrm{A}}{\sqrt{2}}
B) \frac{\mathrm{A}}{2}
C) \sqrt{2} \mathrm{~A}
D) \mathrm{2 A}
326
MediumMHT CET2024
Out of the following musical instruments, which is 'NOT' a percussion instrument?
Options:
A) Daphali
B) Sambal
C) Cymbals
D) Clarinet
327
MediumMHT CET2024
When the tension in string is increased by 3 \mathrm{~kg} \omega \mathrm{t}, the frequency of the fundamental mode increases in the ratio 2: 3. The initial tension in the string is
Options:
A) 1.6 \mathrm{~kg} \omega \mathrm{t}
B) 2.0 \mathrm{~kg} \omega \mathrm{t}
C) 2.4 \mathrm{~kg} \omega \mathrm{t}
D) 2.8 \mathrm{~kg} \omega \mathrm{t}
328
MediumMHT CET2024
A sonometer wire is stretched by hanging a metal bob, the fundamental frequency of the wire is ' n_1 '. When the bob is completely immersed in water, the frequency of vibration of wire becomes ' n_2 '. The relative density of the metal of the bob is
Options:
A) \frac{\mathrm{n}_1-\mathrm{n}_2}{\mathrm{n}_1}
B) \frac{\mathrm{n}_2}{\mathrm{n}_1-\mathrm{n}_2}
C) \frac{\mathrm{n}_1^2}{\mathrm{n}_1^2-\mathrm{n}_2^2}
D) \frac{\mathrm{n}_2^2}{\mathrm{n}_1^2-\mathrm{n}_2^2}
329
MediumMHT CET2024
A tuning fork of frequency 340 Hz is vibrated just above a tube of 120 cm height. Water is slowly poured in the tube. What is the minimum height of water necessary for resonance?
Options:
A) 45 cm
B) 30 cm
C) 35 cm
D) 25 cm
330
MediumMHT CET2024
A stationery wave is represented by y=12 \cos \left(\frac{\pi}{6} x\right) \sin (8 \pi t), where x \& y are in cm and t in second. The distance between two successive antinodes is
Options:
A) 12 cm
B) 10 cm
C) 6 cm
D) 2 cm
331
MediumMHT CET2024
A transverse wave travelling along a stretched string has a speed of 30 \mathrm{~m} / \mathrm{s} and a frequency of 250 Hz . The phase difference between two points on the string 10 cm apart at the same instant is
Options:
A) 0^c
B) \left(\frac{\pi}{2}\right)^c
C) \left(\frac{5 \pi}{3}\right)^c
D) \left(\frac{8 \pi}{3}\right)^c
332
MediumMHT CET2024
A train sounding a whistle of frequency 510 Hz approaches a station at 72 \mathrm{~km} / \mathrm{hr}. The frequency of the note heard by an observer on the platform as the train (1) approaches the station and then (2) recedes the station are respectively (in hertz) (velocity of sound in air =320 \mathrm{~m} / \mathrm{s} )
Options:
A) 544,480
B) 480,544
C) 612,544
D) 544,612
333
MediumMHT CET2024
A set of 28 turning forks is arranged in an increasing order of frequencies. Each fork produces ' x ' beats per second with the preceding fork and the last fork is an octave of the first. If the frequency of the 12^{\text {th }} fork is 152 Hz , the value of ' x ' (no. of beats per second) is
Options:
A) 2
B) 4
C) 6
D) 8
334
MediumMHT CET2024
Two waves \mathrm{Y}_1=0.25 \sin 316 \mathrm{t} \quad and \mathrm{Y}_2=0.25 \sin 310 \mathrm{t} are propagating along the same direction. The number of beats produced per second are
Options:
A) \frac{\pi}{3}
B) \frac{3}{\pi}
C) \frac{2}{\pi}
D) \frac{\pi}{2}
335
MediumMHT CET2024
The distance between two consecutive points with phase difference of 60^{\circ} in wave of frequency 500 Hz is 0.6 m . The velocity with which wave is travelling is
Options:
A) 1.8 \mathrm{~km} / \mathrm{s}
B) 9 \mathrm{~km} / \mathrm{s}
C) 3.6 \mathrm{~km} / \mathrm{s}
D) 2.7 \mathrm{~km} / \mathrm{s}
336
MediumMHT CET2024
A string A has twice the length, twice the diameter, twice the tension and twice the density of another string B. The overtone of A which will have the same fundamental frequency as that of B is
Options:
A) first
B) second
C) third
D) fourth
337
MediumMHT CET2024
A progressive wave of frequency 400 Hz is travelling with a velocity 336 \mathrm{~m} / \mathrm{s}. How far apart are the two points which are 60^{\circ} out of phase?
Options:
A) 0.14 m
B) 0.21 m
C) 0.24 m
D) 0.28 m
338
MediumMHT CET2024
The end correction of resonance tube is 1 cm. If the shortest length resonating with a tuning fork is 15 cm , the next resonating length will be
Options:
A) 35 cm
B) 40 cm
C) 47 cm
D) 64 cm
339
MediumMHT CET2024
If ' l ' is the length of pipe, ' r ' is the internal radius of the pipe and ' v ' is the velocity of sound in air then fundamental frequency of open pipe is
Options:
A) \frac{\mathrm{V}}{2(l+1 \cdot 2 \mathrm{r})}
B) \frac{\mathrm{V}}{(l+1 \cdot 2 \mathrm{r})}
C) \frac{\mathrm{V}}{(l+0.3 \mathrm{r})}
D) \frac{\mathrm{V}}{(l+0 \cdot 6 \mathrm{r})}
340
MediumMHT CET2024
A violin emits sound waves of frequency ' n_1 ' under tension T. When tension is increased by 44 \%, keeping the length and mass per unit length constant, frequency of sound waves becomes ' \mathrm{n}_2 '. The ratio of frequency ' \mathrm{n}_2 ' to frequency ' n_1 ' is
Options:
A) 5: 6
B) 6: 7
C) 6: 5
D) 7: 6
341
MediumMHT CET2024
An observer moves towards a stationary source of sound with a velocity of one-fifth of the velocity of sound. The percentage increase in the apparent frequency is
Options:
A) 5 \%
B) 10 \%
C) 20 \%
D) 25 \%
342
MediumMHT CET2024
The path difference between two waves \mathrm{Y}_1=\mathrm{a}_1 \sin \left(\omega \mathrm{t}-\frac{2 \pi \mathrm{x}}{\lambda}\right) and \mathrm{Y}_2=\mathrm{a}_2 \cos \left(\omega \mathrm{t}-\frac{2 \pi \mathrm{x}}{\lambda}+\phi\right) is
Options:
A) \frac{\lambda \phi}{2 \pi}
B) \frac{\lambda}{2 \pi}\left(\phi+\frac{\pi}{2}\right)
C) \frac{2 \pi}{\lambda}\left(\phi-\frac{\pi}{2}\right)
D) \frac{2 \pi}{\lambda} \phi
343
MediumMHT CET2024
The fundamental frequency of an air column in a pipe open at both ends is ' \mathrm{f}_1 '. Now 80 \% of its length is immersed in water, the fundamental frequency of the air column becomes f_2. The ratio of f_1: f_2 is
Options:
A) 5: 2
B) 4: 5
C) 5: 4
D) 2: 5
344
MediumMHT CET2024
The pitch of a whistle of an engine appears to drop by 30 \% of original value when it passes a stationary observer. If the speed of sound in air is 350 \mathrm{~ms}^{-1}, then the speed of engine in \mathrm{ms}^{-1} is
Options:
A) 840
B) 700
C) 175
D) 150
345
MediumMHT CET2024
The displacement of a wave is given by y=0.002 \sin (100 t+x) where ' x 'and ' y ' are in metre and ' t ' is in second. This represents a wave
Options:
A) of wavelength one metre
B) travelling with a velocity of 100 \mathrm{~m} / \mathrm{s} in the negative x-direction
C) of frequency \left(\frac{100}{\pi}\right) \mathrm{Hz}
D) travelling with a velocity of \left(\frac{50}{\pi}\right) \mathrm{m} / \mathrm{s} in the positive x -direction
346
MediumMHT CET2024
In a vibrating string with fixed ends the waves are of type
Options:
A) stationary longitudinal.
B) stationary transverse.
C) progressive transverse.
D) progressive longitudinal.
347
MediumMHT CET2024
The driver of a car travelling with a speed ' V_1 ' \mathrm{m} / \mathrm{s} towards a wall sounds a siren of frequency ' n ' Hz. If the velocity of sound in air is ' V ' \mathrm{m} / \mathrm{s}, then the frequency of the sound reflected from the wall and as heard by the driver in Hz is
Options:
A) \left(\frac{V_1}{V-V_1}\right) n
B) \left(\frac{V_1-V}{V+V_1}\right) n
C) \left(\frac{V+V_1}{V-V_1}\right) n
D) \left(\frac{V-V_1}{V+V_1}\right) n
348
MediumMHT CET2024
A stretched string is fixed at both ends. It is made to vibrate so that the total number of nodes formed in it is ' x '. The length of the string in terms of the wavelength of waves formed in it is ( \lambda= wavelength )
Options:
A) \frac{\mathrm{X} \lambda}{2}
B) \left(\mathrm{X}+\frac{1}{2}\right) \frac{\lambda}{2}
C) (\mathrm{X}+1) \frac{\lambda}{2}
D) (\mathrm{X}-1) \frac{\lambda}{2}
349
MediumMHT CET2024
A sonometer wire is stretched by hanging a metal bob. The fundamental frequency of vibration of wire is ' n_1 '. When the bob is completely immersed in water, the frequency of vibration of wire becomes ' n_2 '. The relative density of the metal of the bob is
Options:
A) \frac{\mathrm{n}_1}{\mathrm{n}_1-\mathrm{n}_2}
B) \frac{\mathrm{H}_2}{\mathrm{n}_1-\mathrm{n}_2}
C) \mathrm{\frac{n_1^2}{n_1^2-n_2^2}}
D) \frac{\mathrm{n}_2^2}{\mathrm{n}_1^2-\mathrm{n}_2^2}
350
MediumMHT CET2024
Two simple harmonic progressive waves have displacements \rightarrow \mathrm{y}_1=\mathrm{a}_1 \sin \left(\frac{2 \pi \mathrm{x}}{\lambda}-\omega \mathrm{t}\right) and \mathrm{y}_2=\mathrm{a}_2 \cos \left(\frac{2 \pi \mathrm{x}}{\lambda}-\omega \mathrm{t}+\phi\right) What is the phase difference between two waves?
Options:
A) \left(\phi+\frac{\pi}{2}\right)
B) \phi
C) \left(\phi-\frac{\pi}{2}\right)
D) (\phi+\pi)
351
MediumMHT CET2024
A wire under tension 225 N produces 6 beats per second when it is tuned with a fork. When the tension changes to 256 N , it is again tuned with the same tuning fork, the number of beats remain unchanged. The frequency of tuning fork will be
Options:
A) 256 Hz
B) 186 Hz
C) 225 Hz
D) 280 Hz
352
MediumMHT CET2024
Velocity of sound waves in air is 330 \mathrm{~m} / \mathrm{s}. For a particular sound wave in air, path difference of 40 cm is equivalent to phase difference of 1.6 \pi. The frequency of this wave is
Options:
A) 165 Hz
B) 150 Hz
C) 660 Hz
D) 330 Hz
353
MediumMHT CET2024
An air column in a closed organ pipe vibrating in unison with a fork, produces second overtone. The vibrating air column has
Options:
A) three nodes and two antinodes.
B) three nodes and three antinodes.
C) four nodes and three antinodes.
D) three nodes and four antinodes.
354
MediumMHT CET2023
Sound waves of frequency $600 \mathrm{~Hz} fall normally on a perfectly reflecting wall. The shortest distance from the wall at which all particles will have maximum amplitude of vibration is (speed of sound =300 \mathrm{~ms}^{-1}$ )
Options:
A) \frac{1}{4} \mathrm{~m}
B) \frac{1}{8} \mathrm{~m}
C) \frac{3}{8} \mathrm{~m}
D) \frac{7}{8} \mathrm{~m}
355
MediumMHT CET2023
A wire $P Q has length 4.8 \mathrm{~m} and mass 0.06 \mathrm{~kg}. Another wire QR has length 2.56 \mathrm{~m} and mass 0.2 \mathrm{~kg}. Both wires have same radii and are joined as a single wire. This wire is under tension of 80 \mathrm{~N}. A wave pulse of amplitude 3.5 \mathrm{~cm} is sent along the wire \mathrm{PQ} from end \mathrm{P}$. the time taken by the wave pulse to travel along the wire from point P to R is ?
Options:
A) 0.1 s
B) 0.12 s
C) 0.14 s
D) 0.16 s
356
MediumMHT CET2023
A sonometer wire $49 \mathrm{~cm} long is in unison with a tuning fork of frequency 'n'. If the length of the wire is decreased by 1 \mathrm{~cm} and it is vibrated with the same tuning fork, 6 beats are heard per second. The value of 'n$' is
Options:
A) 256 Hz
B) 288 Hz
C) 320 Hz
D) 384 Hz
357
MediumMHT CET2023
A source of sound is moving towards a stationary observer with $\left(\frac{1}{10}\right)^{\text {th }}$ the of the speed of sound. The ratio of apparent to real frequency is
Options:
A) 10: 9
B) 11: 10
C) (11)^2:(10)^2
D) (9)^2:(10)^2
358
MediumMHT CET2023
A string is stretched between two rigid supports separated by $75 \mathrm{~cm}. There are no resonant frequencies between 420 \mathrm{~Hz} and 315 \mathrm{~Hz}$. The lowest resonant frequency for the string is
Options:
A) 210 \mathrm{~Hz}
B) 180 \mathrm{~Hz}
C) 105 \mathrm{~Hz}
D) 1050 \mathrm{~Hz}
359
MediumMHT CET2023
A progressive wave is given by, $\mathrm{Y}=12 \sin (5 \mathrm{t}-4 \mathrm{x}). On this wave, how far away are the two points having a phase difference of 90^{\circ}$ ?
Options:
A) \frac{\pi}{4}
B) \frac{\pi}{8}
C) \frac{\pi}{16}
D) \frac{\pi}{32}
360
MediumMHT CET2023
The equation of the wave is $\mathrm{Y}=10 \sin \left(\frac{2 \pi \mathrm{t}}{30}+\alpha\right) If the displacement is 5 \mathrm{~cm} at \mathrm{t}=0 then the total phase at \mathrm{t}=7.5 \mathrm{~s} will be \left(\sin 30^{\circ}=0.5\right)
Options:
A) \frac{\pi}{3} \mathrm{~rad}
B) \frac{\pi}{2} \mathrm{~rad}
C) \frac{2 \pi}{5} \mathrm{~rad}
D) \frac{2 \pi}{3} \mathrm{~rad}
361
MediumMHT CET2023
If '$l' is the length of the open pipe, 'r' is the internal radius of the pipe and 'V$ ' is the velocity of sound in air then fundamental frequency of open pipe is
Options:
A) \frac{\mathrm{V}}{(l+0.3 \mathrm{r})}
B) \frac{\mathrm{V}}{(l+1.2 \mathrm{r})}
C) \frac{\mathrm{V}}{(l+0.6 \mathrm{r})}
D) \frac{\mathrm{V}}{2(l+1.2 \mathrm{r})}
362
MediumMHT CET2023
When two tuning forks are sounded together, 5 beats per second are heard. One of the forks is in unison with $0.97 \mathrm{~m} length of sonometer wire and the other is in unison with 0.96 \mathrm{~m}$ length of the same wire. The frequencies of the two tuning forks are
Options:
A) 383 \mathrm{~Hz}, 388 \mathrm{~Hz}
B) 475 \mathrm{~Hz}, 480 \mathrm{~Hz}
C) 388 \mathrm{~Hz}, 39 z \mathrm{~Hz}
D) 480 \mathrm{~Hz}, 485 \mathrm{~Hz}
363
MediumMHT CET2023
The equation of a progressive wave is $Y=a \sin 2 \pi\left(n t-\frac{x}{5}\right)$. The ratio of maximum particle velocity to wave velocity is
Options:
A) \frac{\pi a}{5}
B) \frac{2 \pi a}{5}
C) \frac{3 \pi a}{5}
D) \frac{4 \pi a}{5}
364
MediumMHT CET2023
A transverse wave strike against a wall,
Options:
A) its phase changes by $180^{\circ}$ but velocity does not change
B) its phase does not change but velocity changes
C) its velocity changes and phase changes by $180^{\circ}
D) nothing can be predicted about changes in its velocity and phase
365
MediumMHT CET2023
A closed pipe and an open pipe have their first overtone equal in frequency. Then, the lengths of these pipe are in the ratio
Options:
A) 1: 2
B) 2: 3
C) 3: 4
D) 4: 5
366
MediumMHT CET2023
In resonance tube, first and second resonance are obtained at depths $22.7 \mathrm{~cm} and 70.2 \mathrm{~cm}$ respectively. The third resonance will be obtained at a depth
Options:
A) 117.7 cm
B) 92.9 cm
C) 115.5 cm
D) 113.5 cm
367
MediumMHT CET2023
A uniform wire $20 \mathrm{~m} long and weighing 50 \mathrm{~N} hangs vertically. The speed of the wave at mid point of the wire is (acceleration due to gravity =\mathrm{g}=10 \mathrm{~ms}^{-2}$ )
Options:
A) 4 \mathrm{~ms}^{-1}
B) 10 \sqrt{2} \mathrm{~ms}^{-1}
C) 10 \mathrm{~ms}^{-1}
D) Zero $\mathrm{ms}^{-1}
368
MediumMHT CET2023
A passenger is sitting in a train which is moving fast. The engine of the train blows a whistle of frequency '$n'. If the apparent frequency of sound heard by the passenger is 'f$' then
Options:
A) \mathrm{f}=\mathrm{n}
B) \mathrm{f}>\mathrm{n}
C) \mathrm{f < n}
D) \mathrm{f \le n}
369
MediumMHT CET2023
The equation of wave motion is $Y=5 \sin (10 \pi t -0.02 \pi x+\pi / 3) where x is in metre and t$ in second. The velocity of the wave is
Options:
A) 300 m/s
B) 400 m/s
C) 500 m/s
D) 600 m/s
370
MediumMHT CET2023
End correction at open end for air column in a pipe of length '$l' is 'e$'. For its second overtone of an open pipe, the wavelength of the wave is
Options:
A) \frac{2(l+\mathrm{e})}{3}
B) \frac{2(l+2 \mathrm{e})}{3}
C) \frac{4(l+e)}{5}
D) \frac{4(l+2 \mathrm{e})}{5}
371
MediumMHT CET2023
A tuning fork gives 3 beats with $50 \mathrm{~cm} length of sonometer wire. If the length of the wire is shortened by 1 \mathrm{~cm}$, the number of beats is still the same. The frequency of the fork is
Options:
A) 256 Hz
B) 288 Hz
C) 297 Hz
D) 320 Hz
372
MediumMHT CET2023
A tuning fork of frequency $220 \mathrm{~Hz} produces sound waves of wavelength 1.5 \mathrm{~m} in air at N.T.P. The increase in wavelength when the temperature of air is 27^{\circ} \mathrm{C} is nearly \left(\sqrt{\frac{300}{273}}=1.05\right)
Options:
A) 0.06 m
B) 0.10 m
C) 0.09 m
D) 0.07 m
373
MediumMHT CET2023
A uniform string is vibrating with a fundamental frequency '$n$'. If radius and length of string both are doubled keeping tension constant then the new frequency of vibration is
Options:
A) 2 \mathrm{n}
B) 3 \mathrm{n}
C) \frac{\mathrm{n}}{4}
D) \frac{\mathrm{n}}{3}
374
MediumMHT CET2023
The displacement of two sinusoidal waves is given by the equation $\begin{aligned} & \mathrm{y}_1=8 \sin (20 \mathrm{x}-30 \mathrm{t}) \\ & \mathrm{y}_2=8 \sin (25 \mathrm{x}-40 \mathrm{t}) \end{aligned} then the phase difference between the waves after time t=2 \mathrm{~s} and distance x=5 \mathrm{~cm}$ will be
Options:
A) 2 radian
B) 3 radian
C) 4 radian
D) 5 radian
375
MediumMHT CET2023
Two sounding sources send waves at certain temperature in air of wavelength $50 \mathrm{~cm} and 50.5 \mathrm{~cm} respectively. The frequency of sources differ by 6 \mathrm{~Hz}$. The velocity of sound in air at same temperature is
Options:
A) 300 \mathrm{~m} / \mathrm{s}
B) 303 \mathrm{~m} / \mathrm{s}
C) 313 \mathrm{~m} / \mathrm{s}
D) 330 \mathrm{~m} / \mathrm{s}
376
MediumMHT CET2023
41 tuning forks are arranged in increasing order of frequency such that each produces 5 beats/second with next tuning fork. If frequency of last tuning fork is double that of frequency of first fork. Then frequency of first and last fork is
Options:
A) 400,200 \mathrm{~Hz}
B) 200,400 \mathrm{~Hz}
C) 100,200 \mathrm{~Hz}
D) 205,410 \mathrm{~Hz}
377
MediumMHT CET2023
A transverse wave in a medium is given by $y=A \sin 2(\omega t-k x). It is found that the magnitude of the maximum velocity of particles in the medium is equal to that of the wave velocity. What is the value of A$ ?
Options:
A) \frac{2 \lambda}{\pi}
B) \frac{\lambda}{\pi}
C) \frac{\lambda}{2 \pi}
D) \frac{\lambda}{4 \pi}
378
MediumMHT CET2023
A rectangular block of mass '$\mathrm{m}' and crosssectional area A, floats on a liquid of density '\rho'. It is given a small vertical displacement from equilibrium, it starts oscillating with frequency 'n' equal to ( g=$ acceleration due to gravity)
Options:
A) \frac{1}{2 \pi} \sqrt{\frac{\mathrm{Apg}}{\mathrm{m}}}
B) 2 \pi \sqrt{\frac{\mathrm{Apg}}{\mathrm{m}}}
C) \frac{1}{2 \pi} \sqrt{\frac{\mathrm{m}}{\mathrm{Apg}}}
D) 2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{Apg}}}
379
MediumMHT CET2023
A sound of frequency $480 \mathrm{~Hz} is emitted from the stringed instrument. The velocity of sound in air is 320 \mathrm{~m} / \mathrm{s}$. After completing 180 vibrations, the distance covered by a wave is
Options:
A) 60 m
B) 90 m
C) 120 m
D) 180 m
380
MediumMHT CET2023
A sonometer wire '$A' of diameter '\mathrm{d}' under tension 'T' having density '\rho_1' vibrates with fundamental frequency 'n'. If we use another wire 'B' which vibrates with same frequency under tension '2 \mathrm{~T}' and diameter '2 \mathrm{D}' then density '\rho_2' of wire 'B$' will be
Options:
A) \rho_2=2 \rho_1
B) \rho_2=\rho_1
C) \rho_2=\frac{\rho_1}{2}
D) \rho_2=\frac{\rho_1}{4}
381
MediumMHT CET2023
The path difference between two waves, represented by $\mathrm{y}_1=\mathrm{a}_1 \sin \left(\omega \mathrm{t}-\frac{2 \pi \mathrm{x}}{\lambda}\right) and y_2=a_2 \cos \left(\omega t-\frac{2 \pi x}{\lambda}+\phi\right)$ is
Options:
A) \frac{\lambda}{2 \pi}(\phi)
B) \frac{\lambda}{2 \pi}\left(\phi+\frac{\pi}{2}\right)
C) \frac{2 \pi}{\lambda}\left(\phi-\frac{\pi}{2}\right)
D) \frac{2 \pi}{\lambda}(\phi)
382
MediumMHT CET2023
Two progressive waves are travelling towards each other with velocity $50 \mathrm{~m} / \mathrm{s} and frequency 200 \mathrm{~Hz}$. The distance between the two consecutive antinodes is
Options:
A) 0.125 \mathrm{~m}
B) 0.150 \mathrm{~m}
C) 0.175 \mathrm{~m}
D) 0.200 \mathrm{~m}
383
MediumMHT CET2023
A string fixed at both the ends forms standing wave with node separation of $5 \mathrm{~cm}. If the velocity of the wave on the string is 2 \mathrm{~m} / \mathrm{s}$, then the frequency of vibration of the string is
Options:
A) 0.2 Hz
B) 10 Hz
C) 20 Hz
D) 40 Hz
384
MediumMHT CET2023
The second overtone of an open pipe has the same frequency as the first overtone of a closed pipe of length '$L$'. The length of the open pipe will be
Options:
A) \frac{\mathrm{L}}{2}
B) \mathrm{L}
C) 2 \mathrm{~L}
D) 4 \mathrm{~L}
385
MediumMHT CET2023
A car sounding a horn of frequency $1000 \mathrm{~Hz} passes a stationary observer. The ratio of frequencies of the horn noted by the observer before and after passing the car is 11: 9. If the speed of sound is 'v$', the speed of the car is
Options:
A) \mathrm{V}
B) \frac{\mathrm{v}}{2}
C) \frac{\mathrm{v}}{5}
D) \frac{\mathrm{v}}{10}
386
MediumMHT CET2023
A transverse wave $\mathrm{Y}=2 \sin (0.01 \mathrm{x}+30 \mathrm{t}) moves on a stretched string from one end to another end in 0.5 second. If x and y are in \mathrm{cm} and t$ in second, then the length of the string is
Options:
A) 5 m
B) 10 m
C) 15 m
D) 20 m
387
MediumMHT CET2023
The fundamental frequency of air column in pipe 'A' closed at one end is in unison with second overtone of an air column in pipe 'B' open at both ends. The ratio of length of air column in pipe '$\mathrm{A}' to that of air column in pipe '\mathrm{B}$' is
Options:
A) 1: 6
B) 3: 8
C) 2: 3
D) 3: 4
388
MediumMHT CET2023
The equation of wave is $Y=6 \sin \left(12 \pi t-0.02 \pi x+\frac{\pi}{3}\right) where 'x' is in m and 't' in \mathrm{s}$. The velocity of the wave is
Options:
A) 200 \mathrm{~m} / \mathrm{s}
B) 300 \mathrm{~m} / \mathrm{s}
C) 400 \mathrm{~m} / \mathrm{s}
D) 600 \mathrm{~m} / \mathrm{s}
389
MediumMHT CET2023
Two uniform wires of same material are vibrating under the same tension. If the first overtone of first wire is equal to the $2^{\text {nd }} overtone of 2^{\text {nd }} wire and radius of the first wire is twice the radius of the 2^{\text {nd }} wire then the ratio of length of first wire to 2^{\text {nd }}$ wire is
Options:
A) 1: 3
B) 3: 1
C) 1: 9
D) 9: 1
390
MediumMHT CET2023
A uniform rope of length '$L' and mass 'm_1' hangs vertically from a rigid support. A block of mass 'm_2' is attached to the free end of the rope. A transverse wave of wavelength '\lambda_1' is produced at the lower end of the rope. The wavelength of the wave when it reaches the top of the rope is '\lambda_2'. The ratio \frac{\lambda_1}{\lambda_2}$ is
Options:
A) \left[\frac{m_2}{m_1+m_2}\right]^{\frac{1}{2}}
B) \left[\frac{m_1+m_2}{m_2}\right]^{\frac{1}{2}}
C) \left[\frac{\mathrm{m}_1}{\mathrm{~m}_1+\mathrm{m}_2}\right]^{\frac{1}{2}}
D) \left[\frac{\mathrm{m}_2}{\mathrm{~m}_1-\mathrm{m}_2}\right]^{\frac{1}{2}}
391
MediumMHT CET2023
An open organ pipe having fundamental frequency (n) is in unison with a vibrating string. If the tube is dipped in water so that $75 \%$ of the length of the tube is inside the water then the ratio of fundamental frequency of the air column of dipped tube with that of string will be (Neglect end corrections)
Options:
A) 1: 1
B) 2: 1
C) 2: 3
D) 3: 2
392
MediumMHT CET2023
In case of a stationary wave pattern which of the following statement is CORRECT?
Options:
A) The distance between the consecutive nodes is equal to the wavelength.
B) In a pipe at both ends only even harmonics are present in an air column.
C) In a pipe closed at one end, all harmonics are present in an air column.
D) In case of a stretched string when vibrated, frequency of first overtone is same as second harmonic.
393
MediumMHT CET2023
If the length of stretched string is reduced by $40 \% and tension is increased by 44 \%$ then the ratio of final to initial frequencies of stretched string is
Options:
A) 2: 1
B) 3: 2
C) 3: 4
D) 1: 3
394
MediumMHT CET2023
Consider the Doppler effect in two cases. In the first case, an observer moves towards a stationary source of sound with a speed of $50 \mathrm{~m} / \mathrm{s}. In the second case, the observer is at rest and the source moves towards the observer with the same speed of 50 \mathrm{~m} / \mathrm{s}. Then the frequency heard by the observer will be [velocity of sound in air =330 \mathrm{~m} / \mathrm{s}$.]
Options:
A) same in both the cases.
B) more in the second case than in the first case.
C) less in the second case than in the first case.
D) less than the actual frequency in both the cases.
395
MediumMHT CET2023
The equation of simple harmonic progressive wave is given by $y=a \sin 2 \pi(b t-c x). The maximum particle velocity will be half the wave velocity, if \mathrm{c}=
Options:
A) 2 \pi \mathrm{a}
B) \frac{1}{4 \pi \mathrm{a}}
C) \frac{1}{2 \pi \mathrm{a}}
D) 4 \pi \mathrm{a}
396
MediumMHT CET2023
Stationary waves can be produced in
Options:
A) only solid and gaseous media
B) only liquid and gaseous media
C) only solid and liquid media
D) solid, liquid and gaseous media
397
MediumMHT CET2023
If the length of an open organ pipe is $33.3 \mathrm{~cm}, then the frequency of fifth overtone is [Neglect end correction, velocity of sound =333 \mathrm{~m} / \mathrm{s}$ ]
Options:
A) 3500 \mathrm{~Hz}
B) 3000 \mathrm{~Hz}
C) 2500 \mathrm{~Hz}
D) 2000 \mathrm{~Hz}
398
MediumMHT CET2023
If the end correction of an open pipe is $0.8 \mathrm{~cm}$, then the inner radius of that pipe is
Options:
A) \frac{1}{3} \mathrm{~cm}
B) \frac{2}{3} \mathrm{~cm}
C) \frac{3}{2} \mathrm{~cm}
D) 0.2 \mathrm{~cm}
399
MediumMHT CET2023
When both source and listener are approaching each other the observed frequency of sound is given by $\left(V_L\right. and V_S is the velocity of listener and source respectively, \mathrm{n}_0=$ radiated frequency)
Options:
A) \mathrm{n}=\mathrm{n}_0\left[\frac{\mathrm{V}+\mathrm{V}_{\mathrm{L}}}{\mathrm{V}-\mathrm{V}_{\mathrm{s}}}\right]
B) \mathrm{n}=\mathrm{n}_0\left[\frac{\mathrm{V}-\mathrm{V}_{\mathrm{L}}}{\mathrm{V}+\mathrm{V}_{\mathrm{s}}}\right]
C) \mathrm{n}=\mathrm{n}_0\left[\frac{\mathrm{V}-\mathrm{V}_{\mathrm{L}}}{\mathrm{V}-\mathrm{V}_{\mathrm{s}}}\right]
D) \mathrm{n}=\mathrm{n}_0\left[\frac{\mathrm{V}+\mathrm{V}_{\mathrm{L}}}{\mathrm{V}+\mathrm{V}_{\mathrm{s}}}\right]
400
MediumMHT CET2023
Equation of simple harmonic progressive wave is given by $y=\frac{1}{\sqrt{a}} \sin \omega t \pm \frac{1}{\sqrt{b}} \cos \omega t then the resultant amplitude of the wave is \left(\cos 90^{\circ}=0\right)
Options:
A) \frac{a \pm b}{a b}
B) \frac{\sqrt{\mathrm{a}} \pm \sqrt{\mathrm{b}}}{\mathrm{ab}}
C) \frac{\sqrt{\mathrm{a}} \pm \sqrt{\mathrm{b}}}{\sqrt{\mathrm{ab}}}
D) \sqrt{\frac{a+b}{a b}}
401
MediumMHT CET2023
When a string of length '$l' is divided into three segments of length l_1, l_2 and l_3. The fundamental frequencies of three segments are \mathrm{n}_1, \mathrm{n}_2 and \mathrm{n}_3 respectively. The original fundamental frequency 'n$' of the string is
Options:
A) \mathrm{n}=\mathrm{n}_1+\mathrm{n}_2+\mathrm{n}_3
B) \sqrt{\mathrm{n}}=\sqrt{\mathrm{n}_1}+\sqrt{\mathrm{n}_2}+\sqrt{\mathrm{n}_3}
C) \frac{1}{\mathrm{n}}=\frac{1}{\mathrm{n}_1}+\frac{1}{\mathrm{n}_2}+\frac{1}{\mathrm{n}_3}
D) \frac{1}{\sqrt{\mathrm{n}}}=\frac{1}{\sqrt{\mathrm{n}_1}}+\frac{1}{\sqrt{\mathrm{n}_2}}+\frac{1}{\sqrt{\mathrm{n}_3}}
402
MediumMHT CET2023
A closed organ pipe of length '$L_1' and an open organ pipe contain diatomic gases of densities '\rho_1' and '\rho_2$' respectively. The compressibilities of the gases are same in both pipes, which are vibrating in their first overtone with same frequency. The length of the open organ pipe is (Neglect end correction)
Options:
A) \frac{4 \mathrm{~L}_1}{3}
B) \frac{4 L_1}{3} \sqrt{\frac{\rho_1}{\rho_2}}
C) \frac{4 L_1}{3} \sqrt{\frac{\rho_2}{\rho_1}}
D) \frac{3}{4 L_1} \sqrt{\frac{\rho_1}{\rho_2}}
403
MediumMHT CET2022
A stationary wave is represented by $\mathrm{y}=10 \sin \left(\frac{\pi \mathrm{x}}{4}\right) \cos (20 \pi \mathrm{t}) where \mathrm{x} and \mathrm{y} are in \mathrm{cm} and \mathrm{t}$ in second. The distance between two consecutive nodes is
Options:
A) 1 cm
B) 8 cm
C) 4 cm
D) 2 cm
404
MediumMHT CET2022
Two waves are superimposed whose ratio of intensities is $9: 1$. The ratio of maximum and minimum intensity is
Options:
A) 9: 1
B) 4: 1
C) 3: 1
D) 5: 3
405
MediumMHT CET2022
Consider the following statements about stationary waves. A. The distance between two adjacent nodes or antinodes is equal to $\frac{\lambda}{2}(\lambda=$ wavelength of the wave) B. A node is always formed at the open end of the open organ pipe. Choose the correct option from the following.
Options:
A) Both statements A and B are wrong.
B) Only the statement B is true.
C) Only the statement A is true.
D) Both statements A and B are true.
406
MediumMHT CET2022
A hollow pipe of length $0.8 \mathrm{~m} is closed at one end. At its open end, a 0.5 \mathrm{~m} long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of pipe. If the tension in the string is 50 \mathrm{~N} and speed of sound in air is 320 \mathrm{~m} / \mathrm{s}$, the mass of the string is
Options:
A) 20 g
B) 10 g
C) 40 g
D) 5 g
407
MediumMHT CET2021
A cylindrical tube open at both ends has fundamental frequency 'n' in air. The tube is dipped vertically in water so that one-fourth of it is in water. The fundamental frequency of the air column becomes
Options:
A) \frac{3 n}{4}
B) \frac{n}{2}
C) n
D) \frac{2 n}{3}
408
MediumMHT CET2021
Velocity of sound waves in air is '$\mathrm{V}' \mathrm{m} / \mathrm{s}. For a particular sound wave in air, path difference of 'x' \mathrm{cm} is equivalent to phase difference n \pi$. The frequency of this wave is
Options:
A) \frac{V n}{x}
B) \frac{V}{n x}
C) \frac{V n}{2 x}
D) \frac{2 x}{V}
409
MediumMHT CET2021
The length and diameter of a metal wire used in sonometer is doubled. The fundamental frequency will change from 'n' to
Options:
A) \frac{n}{4}
B) 2n
C) 2n
D) \frac{n}{2}
410
MediumMHT CET2021
A closed organ pipe and an open organ pipe of same length produce 2 beats per second when they are set into vibrations together in fundamental mode. The length of open pipe is now halved and that of closed pipe is doubled. The number of beats produced per second will be
Options:
A) 4
B) 3
C) 8
D) 7
411
MediumMHT CET2021
A sonometer wire of length 25 cm vibrates in unison with a tuning fork. When its length is decreased by 1 cm, 6 beats are heard per second. What is the frequency of the tuning fork?
Options:
A) 200 Hz
B) 72 Hz
C) 100 Hz
D) 144 Hz
412
MediumMHT CET2021
Two tuning forks of frequencies $320 \mathrm{~Hz} and 480 \mathrm{~Hz} are sounded together to produce sound waves. The velocity of sound in air is 320 \mathrm{~ms}^{-1}$. The difference between wavelengths of these waves is nearly
Options:
A) 48 cm
B) 16.5 cm
C) 33 cm
D) 42 cm
413
MediumMHT CET2021
When an air column in a pipe open at both ends vibrates such that four antinodes and three nodes are formed, then the corresponding mode of vibration is
Options:
A) first overtone
B) second overtone
C) fourth overtone
D) third overtone
414
MediumMHT CET2021
The wavelength of sound in any gas depends upon
Options:
A) intensity of sound waves only
B) wavelength of sound only
C) density and elasticity of the gas
D) amplitude and frequency of sound
415
MediumMHT CET2021
A uniform rope of length $12 \mathrm{~m} and mass 6 \mathrm{~kg} hangs vertically from the rigid support. A block of mass 2 \mathrm{~kg} is attached to the free end of the rope. A transverse pulse of wavelength 0.06 \mathrm{~m}$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is
Options:
A) 0.8 \mathrm{~m}
B) 0.16 \mathrm{~m}
C) 0.12 \mathrm{~m}
D) 0.4 \mathrm{~m}
416
MediumMHT CET2021
What is the effect of pressure on the speed of sound in a medium, if pressure is doubled at constant temperature?
Options:
A) Remains same
B) Reduced to half
C) Gets doubled
D) Becomes 4 times
417
MediumMHT CET2021
Two sound waves having wavelengths $5.0 \mathrm{~m} and 5.5 \mathrm{~m} propagates in a gas with velocity 300 \mathrm{m} / \mathrm{s}$. The number of heats produced per second is
Options:
A) six
B) two
C) three
D) one
418
MediumMHT CET2021
The frequency of a tuning fork is $220 \mathrm{~Hz} and the velocity of sound in air is 330 \mathrm{~m} / \mathrm{s}$. When the tuning fork completes 80 vibrations, the distance travelled by the
Options:
A) 120 m
B) 60 m
C) 53 m
D) 100 m
419
MediumMHT CET2021
Two waves $\mathrm{Y}_1=0.25 \sin 316 \mathrm{t} and \mathrm{Y}_2=0.25 \sin 310 \mathrm{t}$ are propagation same direction. The number of beats produced per second are
Options:
A) \frac{3}{\pi}
B) \frac{\pi}{3}
C) \frac{\pi}{2}
D) \frac{2}{\pi}
420
MediumMHT CET2021
Two waves are represented by the equation, $\mathrm{y}_1=\mathrm{A} \sin (\omega \mathrm{t}+\mathrm{kx}+0.57) \mathrm{m} and \mathrm{y}_2=\mathrm{A} \cos (\omega \mathrm{t}+\mathrm{kx}) \mathrm{m}, where \mathrm{x} is in metre and \mathrm{t}$ is in second. What is the phase difference between them?
Options:
A) 0.57 radian
B) 1.0 radian
C) 1.57 radian
D) 1.25 radian
421
MediumMHT CET2021
The fundamental frequency of an air column in pipe 'A' closed at one end coincides with second overtone of pipe 'B' open at both ends. The ratio of length of pipe 'A' to that of pipe 'B' is
Options:
A) 3 : 8
B) 3 : 4
C) 1 : 6
D) 2 : 3
422
MediumMHT CET2021
A tuning fork of frequency '$n' is held near the open end of tube which is closed at the other end and the lengths are adjusted until resonance occurs. The first resonance occurs at length L_1 and immediate next resonance occurs at length L_2$. The speed of sound in air is
Options:
A) n\left(L_2-L_1\right)
B) \frac{\mathrm{n}\left(\mathrm{L}_2-\mathrm{L}_1\right)}{2}
C) 2 n\left(L_2-L_1\right)
D) \frac{\mathrm{n}\left(\mathrm{L}_2+\mathrm{L}_1\right)}{2}
423
MediumMHT CET2021
A sound wave of frequency $160 \mathrm{~Hz} has a velocity of 320 \mathrm{~m} / \mathrm{s}. When it travels through air, the particles having a phase difference of 90^{\circ}$, are separated by a distance of
Options:
A) 50 cm
B) 1 cm
C) 25 cm
D) 75 cm
424
MediumMHT CET2021
A glass tube of $1 \mathrm{~m} length is filled with water. The water can be drained out slowly from the bottom of the tube. If vibrating tuning fork of frequency 500 \mathrm{~Hz} is brought at the upper end of the tube then total number of resonances obtained are [Velocity of sound in air is 320 \mathrm{~ms}^{-1}$]
Options:
A) 3
B) 4
C) 1
D) 2
425
MediumMHT CET2021
A sound wave is travelling with a frequency of $50 \mathrm{~Hz}. The phase difference between the two points in the path of a wave is \frac{\pi}{3}. The distance between those two points is (Velocity of sound in air =330 \mathrm{~m} / \mathrm{s}$ )
Options:
A) 1.1 m
B) 0.6 m
C) 2.2 m
D) 1.7 m
426
MediumMHT CET2021
A transverse wave given by $y=2 \sin (0.01 x+30 t) moves on a stretched string from one end to another end in 0.5 second. If 'x' and 'y' are in \mathrm{cm} and '\mathrm{t}$' is in second, then the length of the string is
Options:
A) 6 m
B) 9 m
C) 12 m
D) 15 m
427
MediumMHT CET2021
A pipe open at both ends of length 1.5 m is dipped in water such that the second overtone of vibrating air column is resonating with a tuning fork of frequency 330 Hz. If speed of sound in air is 330 m/s then the length of the pipe immersed in water is (Neglect and correction)
Options:
A) 0.35 m
B) 0.25 m
C) 0.55 m
D) 0.45 m
428
MediumMHT CET2021
A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of $9 \mathrm{~kg} is suspended from the wire. When this mass is replaced by a mass \mathrm{M}, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of 'M$' is
Options:
A) 5 \mathrm{~kg}
B) 12.5 \mathrm{~kg}
C) \frac{1}{25} \mathrm{~kg}
D) 25 \mathrm{~kg}
429
MediumMHT CET2021
Equation of two simple harmonic waves are given by ${Y_1} = 2\sin 8\pi \left( {{t \over {0.2}} - {x \over 2}} \right)m and {Y_2} = 4\sin 8\pi \left( {{t \over {0.16}} - {x \over {1.6}}} \right)m$ then both waves have
Options:
A) same period
B) same frequency
C) same wavelength
D) same velocity
430
MediumMHT CET2021
A pipe closed at one end has length $0.8 \mathrm{~m}. At its open end 0.5 \mathrm{~m} long uniform string is vibrating in its 2^{\text {nd }} harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is 50 \mathrm{~N} and the speed of sound is 320 \mathrm{~m} / \mathrm{s}$, the mass of the string is
Options:
A) 20 gram
B) 10 gram
C) 5 gram
D) 15 gram
431
MediumMHT CET2021
The equation of simple harmonic wave produced in the string under tension $0.4 \mathrm{~N} is given by \mathrm{y=4 \sin (3 x+60 t) ~m}$. The mass per unit length of the string is
Options:
A) 10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}
B) 10^{-5} \mathrm{~kg} \mathrm{~m}^{-1}
C) 10^{-3} \mathrm{~g} \mathrm{~cm}^{-1}
D) 10^{-5} \mathrm{~g} \mathrm{~cm}^{-1}
432
MediumMHT CET2021
A closed organ pipe of length '$\mathrm{L}_c' and an open organ pipe of length '\mathrm{L}_{\mathrm{o}}' contain different gases of densities '\rho_1' and '\rho_2$' respectively. The compressibility of the gases is the same in both the pipes. The gases are vibrating in their first overtone with the same frequency. What is the length of open organ pipe?
Options:
A) \frac{4 L_c}{3} \sqrt{\frac{\rho}{\rho_2}}
B) \frac{3 \mathrm{~L}_{\mathrm{c}}}{4} \sqrt{\frac{\rho_2}{\rho_1}}
C) \frac{4 L_c}{3} \sqrt{\frac{\rho_2}{\rho_1}}
D) \frac{2 L_c}{3} \sqrt{\frac{\rho_2}{\rho}}
433
MediumMHT CET2021
A progressive wave of frequency 50 Hz is travelling with velocity 350 m/s through a medium. The change in phase at a given time interval of 0.01 second is
Options:
A) \frac{\pi}{4}$ rad
B) \frac{3\pi}{2}$ rad
C) \pi$ rad
D) \frac{\pi}{2}$ rad
434
MediumMHT CET2021
A simple harmonic progressive wave is given by $Y=Y_0 \sin 2 \pi\left(n t-\frac{x}{\lambda}\right). If the wave velocity is \left(\frac{1}{8}\right)^{\text {th }}$ the maximum particle velocity then the wavelength is
Options:
A) \frac{\pi Y_0}{2}
B) \frac{\pi Y_0}{4}
C) \frac{\pi \mathrm{Y}_0}{8}
D) \frac{\pi Y_0}{16}
435
MediumMHT CET2021
In fundamental mode, the time required for the sound wave to reach upto the closed end of pipe filled with air is $t$ second. The frequency of vibration of air column is
Options:
A) \frac{1}{t}
B) \frac{2}{t}
C) \frac{3}{t}
D) \frac{0.25}{\mathrm{t}}
436
MediumMHT CET2021
Which one of the following statements is true?
Options:
A) The sound waves in air are longitudinal while the light waves in air are transverse.
B) Both light and sound waves in air are transverse.
C) Both light and sound waves in air are longitudinal.
D) The sound waves are transverse and light waves are longitudinal.
437
MediumMHT CET2021
Two consecutive harmonics of an air column in a pipe closed at one end are of frequencies 150 Hz and 250 Hz. The fundamental frequency of an air column is
Options:
A) 25 Hz
B) 75 Hz
C) 100 Hz
D) 50 Hz
438
MediumMHT CET2021
An air column in a pipe, which is closed at one end will be in resonance with a vibrating tuning fork of frequency 264 Hz for various lengths. Which one of the following lengths is not possible? (V = 330 m/s)
Options:
A) 62.50 cm
B) 93.75 cm
C) 156.25 cm
D) 31.25 cm
439
MediumMHT CET2021
Beats are produced by waves $\mathrm{y_1=a\sin2000\pi t} and \mathrm{y_2=a\sin2008\pi t}$. The number of beats heard per second is
Options:
A) 4
B) 1
C) zero
D) 8
440
MediumMHT CET2021
The frequencies of three tuning forks $\mathrm{A}, \mathrm{B} and \mathrm{C} are related as \mathrm{n}_{\mathrm{A}}>\mathrm{n}_{\mathrm{B}}>\mathrm{n}_{\mathrm{C}}. When the forks \mathrm{A} and \mathrm{B} are sounded together, the number of beats produced per second is 'n_1'. When forks \mathrm{A} and \mathrm{C} are sounded together the number of beats produced per second is 'n_2'. How may beats are produced per second when forks \mathrm{B} and \mathrm{C}$ are sounded together?
Options:
A) \mathrm{n}_1-\mathrm{n}_2
B) \frac{\mathrm{n}_1+\mathrm{n}_2}{2}
C) \mathrm{n}_2-\mathrm{n}_1
D) n_1+n_2
441
MediumMHT CET2021
The equation of wave is given by $\mathrm{y}=10 \sin \left(\frac{2 \pi \mathrm{t}}{30}+\alpha\right). If the displacement is 5 \mathrm{~cm} at \mathrm{t}=0, then the total phase at \mathrm{t}=7.5 \mathrm{~s} will be \left[\sin 30^{\circ}=\cos 60^{\circ}=\frac{1}{2}, \cos 30^{\circ}=\sin 60^{\circ}=\frac{\sqrt{3}}{2}\right]
Options:
A) \frac{\pi}{3} \mathrm{rad}
B) \frac{\pi}{2} \mathrm{rad}
C) \frac{2 \pi}{5} \mathrm{rad}
D) \frac{2 \pi}{3} \mathrm{rad}
442
MediumMHT CET2021
A sonometer wire resonates with 4 antinodes between two bridges for a given tuning fork, when 1 kg mass is suspended from the wire. Using same fork, when mass M is suspended, the wire resonates producing 2 antinodes between the two bridges (distance between two bridges is as before). The value of M is
Options:
A) 2.5 kg
B) 3.5 kg
C) 4 kg
D) 1 kg
443
MediumMHT CET2021
Two wires of same material of radius 'r' and '2r' respectively are welded together end to end. The combination is then used as a sonometer wire under tension 'T'. The joint is kept midway between the two bridges. The ratio of the number of loops formed in the wires such that the joint is a node is
Options:
A) 1 : 5
B) 1 : 2
C) 1 : 4
D) 1 : 3
444
MediumMHT CET2021
The frequency of a tuning fork is 'n' Hz and velocity of sound in air is 'V' m/s. When the tuning fork completes 'x' vibrations, the distance travelled by the wave is
Options:
A) \mathrm{\frac{V}{xn}}
B) \mathrm{\frac{Vn}{x}}
C) \mathrm{\frac{xV}{n}}
D) \mathrm{\frac{x}{Vn}}
445
MediumMHT CET2020
A tuning fork A produces 5 beats per second with a tuning fork of frequency 480 Hz . When a little wax is stuck to a prong of fork A, the number of beats heard per second becomes 2 . What is the frequency of tuning fork A before the wax is stuck to it ?
Options:
A) 475 Hz
B) 482 Hz
C) 478 Hz
D) 485 Hz
446
MediumMHT CET2020
At the poles, a stretched wire of a given length vibrates in unison with a tuning fork. At the equator, for same setting to produce resonance with same fork, the vibrating length of wire
Options:
A) should be same
B) should be increased
C) should be decreased
D) should be 3 times the original length
447
MediumMHT CET2020
A uniform metal wire has length L, mass M and density \rho. It is under tension T and v is the speed of transverse wave along the wire. The area of cross-section of the wire is
Options:
A) \frac{T}{v^2 \rho}
B) \frac{v^2 \rho}{T}
C) T^2 \rho V
D) T v^2 \rho
448
MediumMHT CET2020
The fundamental frequency of a closed pipe is 400 Hz . If \frac{1}{3} rd pipe is filled with water, then the frequency of 2nd harmonic of the pipe will be (neglect and correction)
Options:
A) 1200 Hz
B) 1800 Hz
C) 600 Hz
D) 300 Hz
449
MediumMHT CET2020
A sonometer wire under suitable tension having specific gravity $\rho, vibrates with frequency n$ in air. If the load is completely immersed in water the frequency of vibration of wire will become
Options:
A) \left[\frac{\rho-1}{n \rho}\right]^{\frac{1}{2}}
B) n\left[\frac{\rho-1}{\rho}\right]^{\frac{1}{2}}
C) n\left[\frac{\rho}{\rho-1}\right]^{\frac{1}{2}}
D) \left[\frac{n \rho}{\rho-1}\right]^{\frac{1}{2}}
450
MediumMHT CET2020
An obstacle is moving towards the source with velocity $v. The sound is reflected from the obstacle. If c is the speed of sound and \lambda is the wavelength, then the wavelength of the reflected wave \lambda_r$ is
Options:
A) \lambda_r=\left(\frac{c-v}{c+v}\right) \lambda
B) \lambda_r=\left(\frac{c+v}{c-v}\right) \lambda
C) \lambda_r=\left(\frac{c-v}{c}\right) \lambda
D) \lambda_r=\left(\frac{c+v}{c}\right) \lambda
451
MediumMHT CET2020
An open organ pipe and a closed organ pipe have the frequency of their first overtone identical. The ratio of length of open pipe to that of closed pipe is
Options:
A) 1: 2
B) 3: 4
C) 4: 3
D) 2: 1
452
MediumMHT CET2020
When tension $T is applied to a sonometer wire of length I, it vibrates with the fundamental frequency n. Keeping the experimental setup same, when the tension is increased by 8 N, the fundamental frequency becomes three times the earlier fundamental frequency n$. The initial tension applied to the wire (in newton) was
Options:
A) 2.0
B) 2.5
C) 0.5
D) 1.0
453
MediumMHT CET2020
The extension in a wire obeying Hooke's law is $x. The speed of sound in the stretched wire is v. If the extension in the wire is increased to 4 x$, then the speed of sound in a wire is
Options:
A) 2.5v
B) 2v
C) 1.5v
D) v
454
MediumMHT CET2020
Two waves $Y_1=0.25 \sin 316 t and Y_2=0.25 \sin 310 t$ are propagating along the same direction. The number of beats produced per second are
Options:
A) \frac{\pi}{2}
B) \frac{2}{\pi}
C) \frac{3}{\pi}
D) \frac{\pi}{3}
455
MediumMHT CET2020
Two identical strings of length $l and 2l vibrate with fundamental frequencies \mathrm{N} \mathrm{~Hz} and 1.5 N$ Hz, respectively. The ratio of tensions for smaller length to large length is
Options:
A) 1: 3
B) 1: 9
C) 3: 1
D) 9: 1
456
MediumMHT CET2020
When open pipe is closed from one end third overtone of closed pipe is higher in frequency by $150 \mathrm{~Hz}$, then second overtone of open pipe. The fundamental frequency of open end pipe will be
Options:
A) 400 Hz
B) 200 Hz
C) 500 Hz
D) 300 Hz
457
MediumMHT CET2019
A pipe open at both ends and a pipe closed at one end have same length. The ratio of frequencies of their P^{\text {th }} overtone is
Options:
A) \frac{p+1}{2 p}
B) \frac{p+1}{2 p+1}
C) \frac{2(p+1)}{2 p+1}
D) \frac{p}{2 p+1}
458
MediumMHT CET2019
The fundamental frequency of sonometer wire increases by 9 Hz , if its tension is increased by 69 \%, keeping the length constant. The frequency of the wire is
Options:
A) 42 Hz
B) 24 Hz
C) 30 Hz
D) 36 Hz
459
MediumMHT CET2019
A sonometer wire is in unison with a tuning fork, when it is stretched by weight w and the corresponding resonating length is L_4. If the weight is reduced to \left(\frac{w}{4}\right), the corresponding resonating length becomes L_2. The ratio \left(\frac{L_1}{L_2}\right) is
Options:
A) 4: 1
B) 1: 4
C) 1: 2
D) 2: 1
460
MediumMHT CET2019
For formation of beats, two sound notes must have
Options:
A) different amplitudes and different frequencies
B) exactly equal frequencies only
C) exactly equal amplitudes only
D) nearly equal frequencies and equal amplitudes
461
MediumMHT CET2019
A stretched string fixed at both ends has ' m ' nodes, then the length of the string will be
Options:
A) (m-1) \frac{\lambda}{2}
B) \frac{(m+1) \lambda}{2}
C) \frac{m \lambda}{2}
D) (m-2) \frac{\lambda}{2}
462
MediumMHT CET2019
A stretched wire of length 260 cm is set into vibrations. It is divided into three segments whose frequencies are in the ratio 2: 3: 4. Their lengths must be
Options:
A) 80 \mathrm{~cm}, 60 \mathrm{~cm}, 120 \mathrm{~cm}
B) 120 \mathrm{~cm}, 80 \mathrm{~cm}, 60 \mathrm{~cm}
C) 60 \mathrm{~cm}, 80 \mathrm{~cm}, 120 \mathrm{~cm}
D) 120 \mathrm{~cm}, 60 \mathrm{~cm}, 80 \mathrm{~cm}
463
MediumMHT CET2019
A simple harmonic progressive wave is represented as y=0.03 \sin \pi(2 t-0.01 x) \mathrm{m}. At a given instant of time, the phase difference between two particles 25 m apart is
Options:
A) \pi \mathrm{~rad}
B) \frac{\pi}{2} \mathrm{~rad}
C) \frac{\pi}{4} \mathrm{~rad}
D) \frac{\pi}{8} \mathrm{~rad}
464
MediumMHT CET2019
Find the wrong statement from the following about the equation of stationary wave given by Y=0.04 \cos (\pi x) \sin (50 \pi t) \mathrm{m} where t is in second. Then for the stationary wave.
Options:
A) Time period =0.02 \mathrm{~s}
B) Wavelength =2 \mathrm{~m}
C) Velocity =50 \mathrm{~m} / \mathrm{s}
D) Amplitude =0.02 \mathrm{~m}
465
MediumMHT CET2019
Two open pipes of different lengths and same diameter in which the air column vibrates with fundamental frequencies ' n_1 ', and ' n_2 ' respectively. When both pipes are joined to form a single pipe, its fundamental frequency will be
Options:
A) \frac{n_1+n_2}{n_1 n_2}
B) \frac{n_1 n_2}{2 n_2+n_1}
C) \frac{2 n_2+n_1}{n_1 n_2}
D) \frac{n_1 n_2}{n_1+n_2}
466
MediumMHT CET2019
The equation of simple harmonic progressive wave is given by Y=a \sin 2 \pi(b t-c x). The maximum particle velocity will be twice the wave velocity if
Options:
A) c=\pi a
B) c=\frac{1}{2 \pi a}
C) c=\frac{1}{\pi a}
D) c=2 \pi a
467
MediumMHT CET2019
In a fundamental mode,the time required for the sound wave to reach upto the closed end of a pipe filled with air is ' t ' second. The frequency of vibration of air column is
Options:
A) (2 t)^{-1}
B) 4(t)^{-1}
C) 2(t)^{-1}
D) (4 t)^{-1}
468
MediumMHT CET2019
A transverse wave is propagating on the string. The linear density of a vibrating string is 10^{-3} \mathrm{~kg} / \mathrm{m}. The equation of the wave is Y=0.05 \sin (x+15 t) where x and Y are measured in metre and time in second. The tension force in the string is
Options:
A) 0.2 N
B) 0.250 N
C) 0.225 N
D) 0.325 N
469
MediumNEET2025
A pipe open at both ends has a fundamental frequency f in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to:
Options:
A) \frac{3 f}{2}
B) 2 f
C) \frac{f}{2}
D) f
470
MediumNEET2024
The displacement of a travelling wave $y=C \sin \frac{2 \pi}{\lambda} (at -x) where t is time, x is distance and \lambda$ is the wavelength, all in S.I. units. Then the frequency of the wave is
Options:
A) \frac{2 \pi \lambda}{a}
B) \frac{2 \pi a}{\lambda}
C) \frac{\lambda}{a}
D) \frac{a}{\lambda}
471
MediumNEET2023
The $4^{\text {th }} overtone of a closed organ pipe is same as that of 3^{\text {rd }}$ overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is :
Options:
A) 8 : 9
B) 9 : 7
C) 9 : 8
D) 7 : 9
472
MediumNEET2023
The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is
Options:
A) 2: 1
B) 1: 3
C) 3: 1
D) 1: 2
473
MediumNEET2022
An organ pipe filled with a gas at 27$^\circC resonates at 400 Hz in its fundamental mode. If it is filled with the same gas at 90^\circ$C, the resonance frequency at the same mode will be
Options:
A) 512 Hz
B) 420 Hz
C) 440 Hz
D) 484 Hz
474
MediumNEET2022
If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is
Options:
A) 1 : 1
B) \sqrt2$ : 1
C) 1 : $\sqrt2
D) 1 : 2
475
MediumNEET2020
In a guitar, two strings A and B made of same material are slightly out of tune and produce beats of frequency 6 Hz. When tension in B is slightly decreased, the beat frequency of A is 530 Hz, the original freqnency of B will be :
Options:
A) 524 Hz
B) 536 Hz
C) 537 Hz
D) 523 Hz
476
MediumNEET2018
The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is
Options:
A) 13.2 cm
B) 8 cm
C) 12.5 cm
D) 16 cm
477
MediumNEET2018
A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of 27°C two successive resonances are produced at 20 cm and 73 cm of column length. If the frequency of the tuning fork is 320 Hz, the velocity of sound in air at 27°C is
Options:
A) 330 m s–1
B) 339 m s–1
C) 350 m s–1
D) 300 m s–1
478
MediumNEET2017
Two cars moving in opposite directions approach each other with speed of 22 m s$-1 and 16.5 m s-1 respectively. The driver of the first car blows a horn having a frequency 400 Hz. The frequency heard by the driver of the second car is (velocity of sound is 340 m s-$1)
Options:
A) 361 Hz
B) 411 Hz
C) 448 Hz
D) 350 Hz
479
MediumNEET2017
The two nearest harmonics of a tube closed at one end and open at other end are 220 Hz and 260 Hz. What is the fundamental frequency of the system ?
Options:
A) 20 Hz
B) 30 Hz
C) 40 Hz
D) 10 Hz
480
MediumNEET2016
Three sound waves of equal amplitudes have frequencies (n $-$ 1), n, (n + 1). They superimpose to give beats. The number of beats produced per second will be
Options:
A) 1
B) 4
C) 3
D) 2
481
MediumNEET2016
The second overtone of an open organ pipe has the same frquency as the first overtone of a closed pipe L metre long. The length of the open pipe will be
Options:
A) L
B) 2L
C) {L \over 2}
D) 4L
482
MediumNEET2016
A siren emitting a sound of frequency 800 Hz moves away from an observer towards a cliff at a speed of 15 m s$-1. Then, the frequency of sound that the observer hears in the echo reflected from the cliff is (Take velocity of sound in air = 330 m s-$1)
Options:
A) 838 Hz
B) 885 Hz
C) 765 Hz
D) 800 Hz
483
MediumNEET2016
A uniform rope of length L and mass m1 hangs vertically from a rigid support. A block of mass m2 is attached to the free end of the rope. A transverse pulse of wavelength $\lambda 1 is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is \lambda 2. The ratio \lambda 2/\lambda $1 is
Options:
A) \sqrt {{{{m_2}} \over {{m_1}}}}
B) \sqrt {{{{m_1} + {m_2}} \over {{m_1}}}}
C) \sqrt {{{{m_1}} \over {{m_2}}}}
D) \sqrt {{{{m_1} + {m_2}} \over {{m_2}}}}
484
MediumNEET2016
An air column, closed at one end open at the other, resonates with a tuning fork when the smallest length of the column is 50 cm. The next larger length of the column resonating with the same tuning fork is
Options:
A) 150 cm
B) 200 cm
C) 66.7 cm
D) 100 cm
485
MediumNEET2015
The fundamental frequency of a closed organ pipe of length 20 cm is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is
Options:
A) 120 cm
B) 140 cm
C) 80 cm
D) 100 cm
486
MediumNEET2015
A source of sound S emitting waves of frequency 100 Hz and an observer O are located at some distance from each other. The source is moving with a speed of 19.4 m s$-1 at an angle of 60o with the source observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air 330 m s-$1), is
Options:
A) 106 Hz
B) 97 Hz
C) 100 Hz
D) 103 Hz
487
MediumNEET2015
4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is 5.0 J K$-1 mol-1. If the speed of sound in this gas at NTP is 952 m s-1, then the heat capacity at constant pressure is (Take gas constant R = 8.3 J K-1 mol-$1)
Options:
A) 7.0 J K$-1 mol-$1
B) 8.5 J K$-1 mol-$1
C) 8.0 J K$-1 mol-$1
D) 7.5 J K$-1 mol-$1
488
MediumNEET2015
A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is
Options:
A) 10.5 Hz
B) 105 Hz
C) 155 Hz
D) 205 Hz
489
MediumNEET2014
The number of possible natural oscillations of air column in a pipe closed at one end length 85 cm whose frequencies lie below 1250 Hz are (Velocity of sound = 340 m s$-$1)
Options:
A) 4
B) 5
C) 7
D) 6
490
MediumNEET2014
A speeding motorcyclist sees traffic jam ahead him. He slows down to 36 km hour$-1. He finds that traffic has eased and a car moving ahead of him at 18 km hour-1 is honking at a frequency of 1392 Hz. If the speed of sound is 343 m s-$1, the frequency of the honk as heard by him will be
Options:
A) 1332 Hz
B) 1372 Hz
C) 1412 Hz
D) 1454 Hz
491
MediumNEET2014
If n1, n2 and n3 are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by
Options:
A) {1 \over n} = {1 \over {{n_1}}} + {1 \over {{n_2}}} + {1 \over {{n_3}}}
B) {1 \over {\sqrt n }} = {1 \over {\sqrt {{n_1}} }} + {1 \over {\sqrt {{n_2}} }} + {1 \over {\sqrt {{n_3}} }}
C) \sqrt n = \sqrt {{n_1}} + \sqrt {{n_2}} + \sqrt {{n_3}}
D) n $=$ n1 + n2 + n3
492
MediumNEET2013
The length of the wire between two ends of a sonometer is 100 cm. What should be the positions of two bridges below the wire so that the three segments of the wire have their fundamental frequencies in the ratio 1 : 3 : 5.
Options:
A) {{1500} \over {23}}cm,{{500} \over {23}}cm
B) {{1500} \over {23}}cm, {{300} \over {23}}cm
C) {{300} \over {23}}cm,{{1500} \over {23}}cm
D) {{1500} \over {23}}cm,{{2000} \over {23}}cm
493
MediumNEET2013
Two sources P and Q produce notes of frequency 660 Hz. each. A listener moves from P to Q with a speed of 1 ms$-$1. If the speed of sound is 330 m/s, then the number of beats heard by the listener per second will be
Options:
A) 4
B) 8
C) 2
D) zero
494
MediumNEET2013
A source of unknown frequency gives 4 beats/s when sounded with a source of known frquency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second, when sounded with a source of frequency 513 Hz. The unknown frequency is
Options:
A) 240 Hz
B) 260 Hz
C) 254 Hz
D) 246 Hz
495
MediumNEET2013
If we study the vibration of a pipe open at both ends. then the following statement is not true.
Options:
A) All harmonics of the fundamental frequency will be generated.
B) Pressure change will be maximum at both ends.
C) Open end will be antinode.
D) Odd harmonics of the fundamental frequency will be generated.
496
MediumNEET2013
A wave travelling in the + ve x-direction having displacement along y-direction as 1 m, wavelength 2$\pi m and frequency of {1 \over \pi }$ Hz is represented by
Options:
A) y = sin(10$\pi x - 20\pi $t)
B) y = sin(2$\pi x + 2\pi $t)
C) y = sin(x $-$ 2t)
D) y $= sin(2\pi x - 2\pi $t)
497
MediumNEET2012
A train moving at a speed of 220 m s$-1 towards a stationary object, emits a sound of frequency 1000 Hz. Some of the sound reaching the object gets reflected back to the train as echo. The frequency of the echo as detected by the driver of the train is (Speed of sound in air is 330 m s-$1)
Options:
A) 3500 Hz
B) 4000 Hz
C) 5000 Hz
D) 3000 Hz
498
MediumNEET2012
The equation of a simple harmonic wave is given by y = 3 sin${\pi \over 2}(50t -$ x), where x and y are in metres and t is in seconds. The ratio of maximum particle velocity to the wave velocity is
Options:
A) 2$\pi
B) {3 \over 2}\pi
C) 3\pi
D) {2 \over 3}\pi
499
MediumNEET2012
Two sources of sound placed close to each other, are emitting progressive waves given by y1 = 4sin600$\pi t and y2 = 5sin608\pi $t An observer located near these two sources of sound will hear
Options:
A) 4 beats per second with intensity ratio 25 : 16 between waxing and waning.
B) 8 beats per second with intensity ratio 25 : 16 between waxing and waning.
C) 8 beats per second with intensity ratio 81 : 1 between waxing and warning.
D) 4 beats per second with intensity ratio 81 : 1 between waxing and waning.
500
MediumNEET2012
When a string is divided into three segments of length $l1, l2 and l3 the fundamental frequencies of these three segments are {\upsilon _1},{\upsilon _2} and {\upsilon _3} respectively. The original fundamental frequency (v$) of the string is
Options:
A) \sqrt v = \sqrt {{v_1}} + \sqrt {{v_2}} + \sqrt {{v_3}}
B) v = {v_1} + {v_2} + {v_3}
C) {1 \over v} = {1 \over {{v_1}}} + {1 \over {{v_2}}} + {1 \over {{v_3}}}
D) {1 \over {\sqrt v }} = {1 \over {\sqrt {{v_1}} }} + {1 \over {\sqrt {{v_2}} }} + {1 \over {\sqrt {{v_3}} }}
501
MediumNEET2011
Two identical piano wires, kept under the same tension T have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to occurrence of 6 beats/s when both the wires oscillate together would be
Options:
A) 0.01
B) 0.02
C) 0.03
D) 0.04
502
MediumNEET2011
Sound waves travel at 350 m/s through a warm air and at 3500 m/s through brass. The wavelength of a 700 Hz acoustic wave as it enters brass from warm air
Options:
A) decrease by a factor 10
B) increase by a factor 20
C) increase by a factor 10
D) decrease by a factor 20
503
MediumNEET2011
Two waves are represented by the equations y1 = $asin(\omega t + kx + 0.57) m and y2 = acos(\omega t + kx) m, where x is in meter and t in$ sec. The phase difference between them is
Options:
A) 1.0 radian
B) 1.25 radian
C) 1.57 radian
D) 0.57 radian
504
MediumNEET2010
A tuning fork of frequency 512 Hz makes 4 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per sec when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was
Options:
A) 510 Hz
B) 514 Hz
C) 516 Hz
D) 508 Hz
505
MediumNEET2010
A transverse wave is represented by y = Asin($\omega t -$ kx). For what value of the wavelength is the wave velocity equal to the maximum particle velocity ?
Options:
A) \pi A/2
B) \pi A
C) 2$\pi A
D) A
506
MediumNEET2009
The driver of a car travelling with speed 30 m/s towards a hill sounds a horn of frequency 600 Hz. If the velocity of sound in air is 330 m/s, the frequency of reflected sound as heard by driver is
Options:
A) 555.5 Hz
B) 720 Hz
C) 500 Hz
D) 550 Hz
507
MediumNEET2009
A wave in a string has an amplitude of 2 cm. The wave travels in the +ve direction of x axis with a speed of 128 m/s. and it is noted that 5 complete waves fit in 4m length of the string. The equation describing the wave is
Options:
A) y = (0.02) m sin (15.7 x $-$ 2010t)
B) y = (0.02) m sin (15.7 x + 2010t)
C) y = (0.02) m sin (7.85 x $-$ 1005t)
D) y = (0.02) m sin (7.85 x + 1005t)
508
MediumNEET2009
Each of the two strings of length 51.6 cm and 49.1 cm are tensioned separately by 20 N force. Mass per unit length of both the strings is same and equal to 1 g/m. When both the strings vibrate simultaneously the number of beats is
Options:
A) 7
B) 8
C) 3
D) 5
509
MediumNEET2008
The wave described by y = 0.25 sin(10$\pi x - 2\pi $t), where x and y are in metres and t in seconds, is a wave travelling along the
Options:
A) +ve x direction with frequency 1 Hz and wavelength $\lambda $ = 0.2 m.
B) -ve x direction with amplitude 0.25 m and wavelength \lambda $ = 0.2 m.
C) -$ve x direction with frequency 1 Hz.
D) +ve x direction with frequency $\pi Hz and wavelength \lambda $ = 0.2 m.
510
MediumNEET2008
Two periodic waves of intensities $I1 and I$2 pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is
Options:
A) {\left( {\sqrt {{I_1}} - \sqrt {{I_2}} } \right)^2}
B) 2\left( {{I_1} + {I_2}} \right)
C) {{I_1} + {I_2}}
D) {\left( {\sqrt {{I_1}} + \sqrt {{I_2}} } \right)^2}
511
MediumNEET2008
A point performs simple harmonic oscillation of period T and the equation of motion is given by x = a sin($\omega t + \pi $/6). After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity?
Options:
A) T/3
B) T/12
C) T/8
D) T/6
512
MediumNEET2006
A transverse wave propagating along x-axis is represented by y(x, t) = 8.0 sin (0.5 $\pi x - 4\pi t - \pi $/4) where x is in metres and t is in seconds. The speed of the wave is
Options:
A) 8 m/s
B) 4$\pi $ m/s
C) 0.5$\pi $ m/s
D) \pi $/4 m/s.
513
MediumNEET2006
Two vibrating tuning forks produce waves given by y1 = 4 sin 500$\pi t and y2 = 2 sin506 \pi $t. Number of beats produced per minute is
Options:
A) 360
B) 180
C) 60
D) 3
514
MediumNEET2006
Two sound waves with wavelengths 5.0 m and 5.5. m respectively, each propagate in a gas with velocity 330 m/s. We expect the following number of beats per second.
Options:
A) 6
B) 12
C) 0
D) 1
515
MediumNEET2006
The time of reverberation of a room A is one second. What will be the time (in seconds of reverberation of a room, having all the dimensions double of those of room A ?
Options:
A) 1
B) 2
C) 4
D) 1/2
516
MediumNEET2006
Which one of the following statements is true ?
Options:
A) both light and sound waves can travel in vaccum
B) both light and sound waves in air are transverse
C) The second waves in air are longitudinal while the light waves are transverse
D) both light and sound waves in air are
517
MediumNEET2005
A point source emits sound equally in all directions in a non-absorbing medium. Two points P and Q are at distances of 2 m and 3 m respectively from the source. The ratio of the intensities of the waves at P and Q is
Options:
A) 3 : 2
B) 2 : 3
C) 9 : 4
D) 4 : 9
518
MediumNEET2004
The phase difference between two waves. represented by y1 = 10$-6 sin[100t + (x/50) + 0.5] m y2 = 10-$6 cos[100t + (x/50)] m, where x is expressed in metres and t is exressed in secondss, is approximately.
Options:
A) 1.07 radians
B) 2.07 radians
C) 0.5 radians
D) 1.5 radians
519
MediumNEET2004
A car is moving towards a high cliff. The driver sounds a horn of frequency $f. The reflected sound heard by the driver has frequency 2f$. If v is the velocity of sound, then the velocity of the car, in the same velocity units, will be
Options:
A) v/$\sqrt 2
B) v/3
C) v/4
D) v/2
520
MediumNEET2003
An observer moves towards a stationary source of sound with a speed 1/5th of the speed of sound. The wavelength and frequency of the source emitted are $\lambda and f$ respectively. The apparent frequency and wavelength recorded by the observer are respectively
Options:
A) 1.2 $f, 1.2 \lambda
B) 1.2 $f, \lambda
C) f, 1.2 \lambda
D) 0.8 $f, 0.8 \lambda
521
MediumNEET2002
A wave travelling in positive X-direction with a $= 0.2 ms-2, velocity = 360 ms-1 and \lambda =$ 60 m, then correct expression for the wave is
Options:
A) y = 0.2\sin \left[ {2\pi \left( {6t + {x \over {60}}} \right)} \right]
B) y = 0.2\sin \left[ {\pi \left( {6t + {x \over {60}}} \right)} \right]
C) y = 0.2\sin \left[ {2\pi \left( {6t - {x \over {60}}} \right)} \right]
D) y = 0.2\sin \left[ {\pi \left( {6t - {x \over {60}}} \right)} \right]
522
MediumNEET2002
A whistle revolves in a circle with angular speed $\omega = 20 rad/s using a string of length 50 cm. If the frequency of sound from the whistle is 385 Hz, then what is the minimum frequency heard by an observer which is far away from the centre (velocity of sound =$ 340 m/s)
Options:
A) 385 Hz
B) 374 Hz
C) 394 Hz
D) 333 Hz.
523
MediumNEET2001
The equation of a wave is represented by y $= 10-4 sin(100t - {x \over {10}}$) m. then the velocity of wave will be
Options:
A) 100 m/s
B) 4 m/s
C) 1000 m/s
D) 10 m/s
524
MediumNEET2001
If the tension and diameter of a sonometer wire of fundamental frequency n is doubled and density is halved then its fundamental frequency will become
Options:
A) {\pi \over 4}
B) \sqrt 2 n
C) n
D) {n \over {\sqrt 2 }}
525
MediumNEET2001
Two waves having equation x1 = $asin(\omega t - kx + \phi 1), x2 = asin(\omega t -kx + \phi $2). If in the resultant wave the frequency and amplitude remain equal to amplitude of superimposing waves, the phase difference between them is
Options:
A) {\pi \over 6}
B) {{2\pi } \over 3}
C) {\pi \over 4}
D) {\pi \over 3}
526
MediumNEET2000
A string is cut into three parts, having fundamental frequencies n1, n2, n3 respectively. Then original fundamental frequency n related by the expression as
Options:
A) {1 \over n} = {1 \over {{n_1}}} + {1 \over {{n_2}}} + {1 \over {{n_3}}}
B) n = {n_1} \times {n_2} \times {n_3}
C) n $=$ n1 + n2 + n3
D) n = {{{n_1} + {n_2} + {n_3}} \over 3}
527
MediumNEET2000
Two stationary sources each emitting waves of wavelength $\lambda $, an observer moves from one source to another with velovcity u. Then number of beats heard by him
Options:
A) {{2u} \over \lambda }
B) {u \over \lambda }
C) \sqrt {u\lambda }
D) {u \over {2\lambda }}
528
MediumNEET2000
The equations of two waves acting in perpendicular directions are given as x = $acos(\omega t +\delta ) and y = acos(\omega t + \alpha ), where \delta = \alpha + {\pi \over 2}$, the resultant wave represents
Options:
A) a parabola
B) a circle
C) an ellipse
D) a straight line
529
MediumVITEEE2024
In the equation for a stationary wave given by y=5 \cos \frac{\pi x}{25} \sin 100 \pi t. Here, x is in cm and t in second. A node will not occur at distance x is equal to
Options:
A) 25 cm
B) 62.5 cm
C) 12.5 cm
D) 37.5 cm
530
MediumVITEEE2023
The frequency of a sonometer wire is $100 \mathrm{~Hz} When the weights producing the tensions are completely immersed in water, the frequence becomes 60 \mathrm{~Hz} and on immersing the weights in a certain liquid, the frequency becomes 40 \mathrm{~Hz}$. The specific gravity of the liquid is
Options:
A) 1.42
B) 1.31
C) 1.82
D) 1.21
531
MediumVITEEE2022
A man stands between two parallel cliffs (not in middle). When he claps his hands, he hears two echoes one after is and the other after $2 \mathrm{~s}. If the velocity of sound in air is 330 \mathrm{~m} / \mathrm{s}$, the width of the cliff is
Options:
A) 330 m
B) 495 m
C) 660 m
D) 990 m
531
Total Questions
52
Easy
473
Medium
6
Hard
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