Question

A source of sonic oscillations with frequency $n=1700Hz$ and a receiver are located on the same normal to a wall. Both the source and the receiver are stationary, and the wall recedes from the source with velocity $u=6.0cm/s$. Then the beat frequency registered by the receiver is approximately (velocity of sound is $v=340m/s$)

• A. $0.6Hz$
• B. $6.0Hz$
• C. $3.0Hz$
• D. $0.3Hz$

Answer 1

The correct option is A $0.6Hz$


As both source and receiver are at rest, the frequency of sound waves which directly reach receiver will be $n_0\left(1700Hz\right)$.

The frequency of sound which the wall will receive as a moving observer is

$n_1=n_0\left[\frac{v}{v+u}\right]$

The wall now behaves as a moving source of frequency $n_1$. When the sound reflected by the wall is received by the receiver, the frequency observed is

$n_2=n_1\left[\frac{v-u}{v}\right]=n_0\left(\frac{v-u}{v+u}\right)$
$=1700\left[\frac{340-0.06}{340+0.06}\right]$
$=1700\times \frac{339.94}{340.06}=1699.4Hz$

Thus beat frequency received by detector is $\Delta n=1700-1699.4$
$=0.6Hz$.