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 number of waves encountered by the moving plane per unit time is given by 

$n=\frac{dis\tan cetravelled}{wavelength}$

$=\frac{c+v}{\lambda }=\frac{c}{\lambda }\left(1+\frac{v}{c}\right)=f\left(1+\frac{v}{c}\right)$

The stationary observer meets the frequency $f^{\text{'}}$ of the incident wave and receives the reflected wave of frequency $f^{\text{'}\text{'}}$emitted by the moving platform as 

$f^{\text{'}\text{'}}=\frac{f^{\text{'}}}{1-v/c}=\frac{f\left(1+v/c\right)}{1-v/c}=\frac{f\left(c+v\right)}{\left(c-v\right)}$

wavelength of the reflected wave 

$\lambda \text{'}=\frac{c-v}{f\text{'}\text{'}}=\left(\frac{c-v}{c+v}\right)\frac{c}{f}$

Beat frequency $=f^{\text{'}\text{'}}-f$