A sound wave of frequency `f` travels horizontally to the right. It is reflected from a large vertical plane surface moving to left with a speed `v`. The speed of sound in medium is `C`

Options

A. The frequency of the reflected wave is `(f(c + v))/(c - v)`
B. The wavelength of the reflected wave is `(c(c - v))/(f(c + v))`
C. The number of waves striking the surface per second is `(f(c + v))/(c )`
D. The number of beats heard by a stationary listener to the left of the reflection surface is `(f v)/(c - v)`

Answer

D

Explanation

Frequency of reflected wave
`f_(r ) =f((c+v)/(c-v))`, (1) is O.K.
`lambda_(r ) = ( c)/(f_(r )) = (c(c-v))/(f(c+v))`, (2) is O.K.
Frequency received at surface
`f_(1) = f((c+v)/(c ))`, (3) is O.K.
Statinoary listener `L`: Hw will receive `f`, directly, and `f_(1)` from surface (surface will act as source)
`f'_(1) = f_(1)[(c )/(c-v)] = f((c+v)/(c-v))`
Beat frequency `= f'_(1) - f = f[(c+v)/(c-v) -1]`
`= f[(2v)/(c-v)] = (2f v)/(c-v)`
(4) is wrong.