Question

A stationary source emits the sound of frequency $f_{0}=492 \, Hz$ . The sound is reflected by a large car approaching the source with a speed of $2 \, m \, s^{- 1}$ . The reflected signal is received by the source and superposed with the original. What will be the beat frequency of the resulting signal in Hz? (Given that the speed of sound in air is 330 $m \, s^{- 1}$ and the car reflects the sound at the frequency it has received).

Answer 1

Frequency of sound as received by large car approaching the source.
$f_{1}=\frac{C + V_{0}}{C} \, f_{0}=\left(\frac{330 + 2}{330}\right)492 \, Hz.$
This car now acts as source for reflected sound wave
$\therefore \, \, f_{r e f l e c t e d}=f_{1}$
Frequency of sound received by source,
$f_{2}=\left(\frac{C}{C - V_{0}}\right) \, f_{r e f l e c t e d}=\left(\frac{330}{330 - 2}\right)\times f_{1}=\frac{330}{328}\times \frac{332}{330}\times 492Hz$
$\therefore \, $ Beat frequency $=\left|f_{0} - f_{2}\right|=\left(\frac{332}{328} - 1\right)\times 492 \, Hz$
$=6 \, Hz$