Physics - Sound Wave Question with Solution | TestHub

Given equations of waves are $Y_1=0.25\sin 316t$ and $Y_2=0.25\sin 310t$.

Comparing with the standard wave equation $Y=A\sin \omega t$, the angular frequencies are:

${\omega }_1=316$ rad/s

${\omega }_2=310$ rad/s

The corresponding frequencies are:

$f_1=\frac{{\omega }_1}{2\pi }=\frac{316}{2\pi }=\frac{158}{\pi }$ Hz

$f_2=\frac{{\omega }_2}{2\pi }=\frac{310}{2\pi }=\frac{155}{\pi }$ Hz

The number of beats produced per second is given by the difference in frequencies:

$f_{beat}=f_1-f_2=\frac{158}{\pi }-\frac{155}{\pi }=\frac{3}{\pi }$

Answer: $\frac{3}{\pi }$