A sound wave of frequency n travels horizontally to the right with speed 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

Options

A. zero
B. `(n(c+v))/(c-v)`
C. `(nv)/(c-v)`
D. `(2nv)/(c-v)`

Answer

D

Explanation

Initially wall behaves as an approaching observer, so frequency of sound reaching the wall is
`n_1=(c+v)/(c )n`
while reflecting, the wall behaves as an approaching source, so frequency received by stationary observer is
`n_2=(c)/(c-v)n_1=(c)/(c-v)xx(c+v)/(c)n=(c+v)/(c-v)n`
Direct frequency received by observer in n. the number of beats is
`x=n_2-n=(c+v)/(c-v)n-n=(2nv)/(c-v)`