Question 450: Waves

Question

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 60
o
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

Accepted Answer

Here, original frequency of sound, f
0
= 100 Hz
Speed of source V
s
= 19.4 cos 60ÃÂ° = 9.7
From Doppler's formula
$${f^1} = {f_0}\left( {{{V - {V_0}} \over {V - {V_S}}}} \right)$$
$${f^1} = 100\left( {{{V - 0} \over {V - \left( { + 9.7} \right)}}} \right)$$
$${f^1} = 100{V \over {V\left( {1 - {{9.7} \over V}} \right)}} = {{100} \over {\left( {1 - {{9.7} \over {330}}} \right)}}$$
= 103Hz
Apparent frequency f
1
= 103 Hz

Answer

106 Hz

Answer

97 Hz

Answer

100  Hz

Answer

103 Hz

Waves

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