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(D) The given wave equations are $y_1 = 4 \sin(708 \pi t)$ and $y_2 = 3 \sin(700 \pi t)$.Comparing these with the standard equation $y = A \sin(2 \pi

Vedclass · Accepted Answer

$4, 49:1$

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(D) The given wave equations are $y_1 = 4 \sin(708 \pi t)$ and $y_2 = 3 \sin(700 \pi t)$.Comparing these with the standard equation $y = A \sin(2 \pi f t)$, we get:For $y_1$: $2 \pi f_1 = 708 \pi \implies f_1 = 354 	ext{ Hz}$ and amplitude $A_1 = 4$.For $y_2$: $2 \pi f_2 = 700 \pi \implies f_2 = 350 	ext{ Hz}$ and amplitude $A_2 = 3$.Beat frequency $f_b = |f_1 - f_2| = |354 - 350| = 4 	ext{ beats per second}$.The intensity $I$ is proportional to the square of the amplitude $(I \propto A^2)$.Maximum intensity (waxing) $I_{max} \propto (A_1 + A_2)^2 = (4 + 3)^2 = 7^2 = 49$.Minimum intensity (wanning) $I_{min} \propto (A_1 - A_2)^2 = (4 - 3)^2 = 1^2 = 1$.Therefore, the ratio of intensity between waxing and wanning is $I_{max} : I_{min} = 49:1$.The number of beats per second is $4$ and the intensity ratio is $49:1$.

Two sources of sound are emitting progressive waves $y_1 = 4 \sin 708 \pi t$ and $y_2 = 3 \sin 700 \pi t$. The sources are placed close to each other. The number of beats heard per second and intensity ratio between waxing and wanning are respectively

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