Physics - Sound Wave Question with Solution | TestHub

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

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

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

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

The frequencies of the two waves are:

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

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

The number of beats produced per second is the difference between the two frequencies:

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

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