Two sources of sound placed close to each oth | vedclass

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(B) The given wave equations are $y_1 = 4 \sin(600\pi t)$ and $y_2 = 5 \sin(608\pi t)$.Comparing these with the standard form $y = A \sin(2\pi f t)$,w

Vedclass · Accepted Answer

$4$ beats per second with intensity ratio $81:1$ between waxing and waning.

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(B) The given wave equations are $y_1 = 4 \sin(600\pi t)$ and $y_2 = 5 \sin(608\pi t)$.Comparing these with the standard form $y = A \sin(2\pi f t)$,we get:$2\pi f_1 = 600\pi \implies f_1 = 300 	ext{ Hz}$.$2\pi f_2 = 608\pi \implies f_2 = 304 	ext{ Hz}$.The beat frequency is $f_{beat} = |f_2 - f_1| = |304 - 300| = 4 	ext{ beats per second}$.The maximum amplitude is $A_{max} = A_1 + A_2 = 4 + 5 = 9$.The minimum amplitude is $A_{min} = |A_2 - A_1| = |5 - 4| = 1$.The intensity ratio is given by $\frac{I_{max}}{I_{min}} = \frac{A_{max}^2}{A_{min}^2} = \frac{9^2}{1^2} = \frac{81}{1}$.

Two sources of sound placed close to each other are emitting progressive waves given by $y_1 = 4 \sin(600\pi t)$ and $y_2 = 5 \sin(608\pi t)$. An observer located near these two sources of sound will hear:

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