Question

A source of the sound of frequency. $256Hz$ is moving rapidly towards a wall with a speed of $5m/s$. How many beats per second will be heard If sound travels at a speed of $330m/s$?

Answer 1

Beat frequency will be observed at the source due to the presence of two frequencies there. one is its own original frequency and other will be the echo which will come after striking the wall.

Let there be an imaginary observer $\left(0_1\right)$ at the wall frequency observed by $0_1$ (due to doppler effect ) $=\left(\frac{V_{sound}}{V_{sound}-V_{source}}\right)f_0$

$=\left(\frac{330}{330-5}\right)\left(256\right)\simeq 260$

Now, the sound after striking the wall will go to source (echo)

Frequency of echo an observed by the source (due to doppler effect ) $=\left(\frac{V_{sound}+5}{V_{sound}}\right)\left(260\right)$

$=\left(\frac{330+5}{330}\right)\left(260\right)\simeq 264$

$\Rightarrow$ Beat frequency $=|f_{echo}-f_0|=8$

$=8$ beat per second.

Hence, the answer is $8$ beat per second.