Question

A stationary sound source $‘S^{\prime }$ of frequency $334\text{Hz}$ and a stationary observer $‘O^{\prime }$ are placed near a reflecting surface moving away from the source with velocity $2\text{m/s}$ as shown in the figure. If the velocity of the sound waves in air is $V=330\text{m/s}$, the apparent frequency (in $\text{Hz}$) of the echo is

Answer 1

Frequency of sound recieved at the reflecting surface is
$f^{\prime }=\left(\frac{v-v_0}{v}\right)f$
Frequency of reflected sound, percieved by the observer is
$f"=\left(\frac{v}{v+v_s}\right)f^{\prime }$
$f"=\left(\frac{v-v_0}{v+v_s}\right)f\because v_0=v_s$
$f"=\left(\frac{330-2}{330+2}\right)\times 334=330\text{Hz}$