Question

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. The incorrect statement is

• A. The number of wave striking the surface per second is $f\frac{(c+v)}{c}$
• B. The wavelength of reflected wave is $\frac{c(c-v)}{f(c+v)}$
• C. The frequency of reflected wave is $\frac{f(c+v)}{(c-v)}$
• D. The number of beats heard by a stationary listener to the left of the reflecting surface is $\frac{vf}{(c-v)}$

Answer 1

The correct option is D The number of beats heard by a stationary listener to the left of the reflecting surface is $\frac{vf}{(c-v)}$

Number of waves encountered by the moving plane per unit time =$\frac{distancetravelled}{wavelength}$
$=\frac{c+v}{\lambda }=\frac{c}{\lambda }=f(1+\frac{v}{c})$
f' is the frequency of the incident wave and f” is the frequency of the reflected wave that a stationary observer meets.
$f"=\frac{f^{\prime }}{\left(\frac{1-v}{c}\right)}=\frac{f\left(\frac{1+v}{c}\right)}{\left(\frac{1-v}{c}\right)}=\frac{f(c+v)}{(c-v)}$
$\lambda "=\frac{c}{f"}=\frac{c}{f}\left(\frac{c-v}{c+v}\right)$
Beat frequency =f" =f
$=\frac{f\left(\frac{1+v}{c}\right)}{\left(\frac{1-v}{c}\right)}-f\frac{2vf}{(c-v)}$