The displacement equations of sound waves pro | vedclass

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(D) The given equations are $y_1 = 5 \sin(400 \pi t)$ and $y_2 = 8 \sin(408 \pi t)$.Comparing these with the standard equation $y = A \sin(\omega t)$,

Vedclass · Accepted Answer

$240$

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(D) The given equations are $y_1 = 5 \sin(400 \pi t)$ and $y_2 = 8 \sin(408 \pi t)$.Comparing these with the standard equation $y = A \sin(\omega t)$, we get angular frequencies $\omega_1 = 400 \pi 	ext{ rad/s}$ and $\omega_2 = 408 \pi 	ext{ rad/s}$.The frequencies of the two waves are $f_1 = \frac{\omega_1}{2 \pi} = \frac{400 \pi}{2 \pi} = 200 	ext{ Hz}$ and $f_2 = \frac{\omega_2}{2 \pi} = \frac{408 \pi}{2 \pi} = 204 	ext{ Hz}$.The beat frequency is the difference between the two frequencies: $f_b = |f_2 - f_1| = |204 - 200| = 4 	ext{ beats per second}$.To find the number of beats per minute, we multiply the beat frequency by $60 	ext{ seconds}$:$	ext{Beats per minute} = 4 	imes 60 = 240 	ext{ beats/min}$.

The displacement equations of sound waves produced by two sources are given by $y_1 = 5 \sin(400 \pi t)$ and $y_2 = 8 \sin(408 \pi t)$, where $t$ is time in seconds. If the waves are produced simultaneously, the number of beats produced per minute is

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