Question

Three sound waves of equal amplitudes have frequencies $(v-1),v,(v+1)$. They superpose to give beats. The number of beats produced per second will be

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

The correct option is C $2$

$p_1=p_0\sin 2\pi (x-1)t{p}_2=p_0\sin 2\pi \left(x\right)t{p}_3=p_0\sin 2\pi (x+1)tp=p_1+p_3+p_2$
$=p_0\sin 2\pi (x-1)t+p_0\sin 2\pi (x+1)t+p_0\sin 2\pi xt$
$=2p_0\sin 2\pi xt\cos 2\pi t+p_0\sin 2\pi xt=p_0\sin 2\pi xt[2\cos \pi t+1]$

$f_{beat}=2$