Question

A car has source of sound of frequency $256\text{Hz}$ is moving rapidly towards wall with a velocity of $5\text{m/sec}$. How many beats per second will be heard by the driver, if sound travels at a speed of 330 m/sec?

Answer 1

If the reflector of sound is stationary, the image of the source in the reflecting surface will act as the source of reflected sound.
$f^{\prime }=f\frac{(v+v_0)}{(v-v_s)}$
The observer travels with the sound source
$f^{\prime }=256\frac{(330+5)}{(330-5)}$
$f^{\prime }=\frac{256\times 335}{335}=264$
$\therefore$ Beat frequency $=f^{\prime }-f=264-256=8\text{Hz}$