Question

A sound wave of frequency n travels horizontally to the right with speed c. It is reflected from a broad wall moving to the left with speed v. The number of beats heard by a stationary observer to the left of the wall is

• A. zero
• B. $\frac{n(c+v)}{c-v}$
• C. $\frac{nv}{c-v}$
• D. $\frac{2nv}{c-v}$

Answer 1

The correct option is D $\frac{2nv}{c-v}$

Initially wall behaves as an approaching observer, so frequency of sound reaching the wall is
$n_1=\frac{c+v}{c}N$
while reflecting, the wall behaves as an approaching source, so frequency received by stationary observer is
$n_2=\frac{c}{c-v}{n}_1=\frac{c}{c-v}\times \frac{c+v}{c}n=\frac{c+v}{c-v}n$
Direct frequency received by observer is n. the number of beats is
$x=n_2-n=\frac{c+v}{c-v}n-n=\frac{2nv}{c-v}$