Question

A tuning fork of frequency 256 Hz is moving towards a well with a velocity of 5 m/s. If the speed of sound is 330 m/s, then the number of beats heard per second by a stationary observer lying between tuning fork and the wall is :

• A. 2
• B. 4
• C. zero
• D. 8

Answer 1

The correct option is C zero

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 $v_{sound}=330m/s$

Velocity of the source $v_{source}=5m/s$

Doppler effect when a source moves towards the stationary observer:

$n_d=n[\frac{v_{sound}}{v_{sound}-v_{source}}]$ $=256[\frac{330}{330-5}]=260Hz$

Doppler effect when a source moves towards the wall:

$n^{\prime }=n[\frac{v_{sound}}{v_{sound}-v_{source}}]$ $=256[\frac{330}{330-5}]=260Hz$

Now apparent frequency after the reflection from the wall $n^{\prime \prime }=n^{\prime }=260Hz$

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