Question 454: Waves

Question

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

Accepted Answer

To determine the number of beats produced per second by two waves, we need to calculate the difference in their frequencies. The beat frequency is given by the absolute difference between the frequencies of the two waves. In the given equations, $$Y_1=0.25 \sin 316 t$$ and $$Y_2=0.25 \sin 310 t$$, the numerical coefficients in front of $$t$$ represent the angular frequency $$\omega$$ of each wave, since the general form of a wave equation is $$y = A \sin(\omega t + \phi)$$, where $$A$$ is the amplitude, $$\omega$$ is the angular frequency, $$t$$ is the time, and $$\phi$$ is the phase angle.
The angular frequency $$\omega$$ is related to the frequency $$f$$ of the wave by the equation $$\omega = 2\pi f$$. Thus, to find the frequencies ($$f_1$$ and $$f_2$$) of the waves $$Y_1$$ and $$Y_2$$, we have:
For $$Y_1$$: $$316 = 2\pi f_1 \Rightarrow f_1 = \frac{316}{2\pi} = \frac{158}{\pi}$$ Hz.
For $$Y_2$$: $$310 = 2\pi f_2 \Rightarrow f_2 = \frac{310}{2\pi} = \frac{155}{\pi}$$ Hz.
The beat frequency $f_{	ext{beat}}$ is the difference between $f_1$ and $f_2$:
$f_{	ext{beat}} = |f_1 - f_2| = \left| \frac{158}{\pi} - \frac{155}{\pi} ight| = \frac{|158 - 155|}{\pi} = \frac{3}{\pi} \, 	ext{Hz}$
Thus, the number of beats produced per second is $$\frac{3}{\pi}$$, which corresponds to
Option C
.

Answer

$$\frac{\pi}{2}$$

Answer

$$\frac{2}{\pi}$$

Answer

$$\frac{3}{\pi}$$

Answer

$$\frac{\pi}{3}$$

Waves

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

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