A sound wave emitted from a stationary source of frequency f travels horizontally to the right with a speed v. It is reflected from a large vertical plane surface moving to left with a speed v. The speed of sound in medium is c. Choose the correct options.

The number of waves encountered by the moving plane per unit time is given by
$\mathrm{f}\text{'}=\frac{\text{ distance travelled }}{\text{ wavelength }}=\frac{\mathrm{c}+\mathrm{v}}{\mathrm{\lambda }}=\frac{\mathrm{c}}{\mathrm{\lambda }}\left(1+\frac{\mathrm{v}}{\mathrm{c}}\right)=\mathrm{f}\left(1+\frac{\mathrm{v}}{\mathrm{c}}\right)$
The stationary observer meets the frequency f of the incident wave and receives the reflected wave of frequency f '' emitted by the moving platform as

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

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

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

$\frac{f\left(1+\frac{v}{c}\right)}{\left(1-\frac{v}{c}\right)}-f=\frac{2vf}{c-v}$