A sound wave of frequency v travels horizontally to right. It is reflected from a large vvertical plane surface moving to the left with a speed v. The speed of sound in the medium is c, then

Options

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

Answer

A

Explanation

Number of waves striking the surface per second (or the frequency of the waves reaching surface of the moving target)
`n'=((c+v))/(lambda)=(v(c+v))/(c)`
Now, these waves are reflected by the moving target (Which now act as a source). Therefore, apparent frequency of reflected second
`n''=((c)/(c-v))n'=v((c+v)/(c-v))`
The wavelength of reflected wave
`=(c)/(n'')=(c(c-v))/(v(c+v))`
The number of beats heard by stationary listener `=n''-v=v`
`((c+v)/(c-v))-v=(2"vv")/((c-v))`
Hence, option (a) is correct.