Question

A source of sound of frequency 512 Hz is moving towards a wall with velocity $v$ equal to that of second. An observer is standing between the source and the wall, then he will listen :

• A. no beats $s^{-1}$
• B. 3 beats $s^{-1}$
• C. 6 beats $s^{-1}$
• D. 12 beats $s^{-1}$

Answer 1

The correct option is A no beats $s^{-1}$

Let $n_d$ and $n^{\prime \prime }$ be the frequencies heard by the observer O coming directly from the tuning fork and after reflecting from the wall respectively.

Velocity of sound in air $=v_{sound}m/s$

Velocity of the source $=v_{source}m/s$

Doppler effect when a source moves towards the stationary observer:

$n_d=512[\frac{v_{sound}}{v_{sound}-v_{source}}]$

Doppler effect when a source moves towards the wall:

$n^{\prime }=512[\frac{v_{sound}}{v_{sound}-v_{source}}]$

Now apparent frequency after the reflection from the wall $n^{\prime \prime }=n^{\prime }=512[\frac{v_{sound}}{v_{sound}-v_{source}}]$

Beat frequency heard by the observer $b=n_d-n^{\prime \prime }=0$