Question

A source is moving towards observer with a speed of 20 m/s and having frequency 240 Hz and observer is moving towards source with a velocity of 20 m/s. what is the apparent frequency heard by observer, if velocity of sound is 340 m/s?

• A. 270 Hz
• B. 240 Hz
• C. 268 Hz
• D. 360 Hz

Answer 1

The correct option is A 270 Hz

Key Idea the perceived frequency heard by the observer depends upon the relative motion between observer and source.
If the source and observer are approaching each other, then the velocity of the source $v_s$ is positive and velocity of the listener $v_l$ is negative, the perceived frequency will be higher than the original.
Perceived frequency is given by
$n^{\prime }=n\left(\frac{v+v_0}{v-v_0}\right)$ $[\because n^{\prime }=n\frac{v-(-v_0}{v-v_s}]$
Here, $v=340m/s,v_0=20m/s,$
$v_s=20m/s,n=240Hz$
Hence, $n^{\prime }=240\left(\frac{340+20}{340-20}\right)$
$=240\times \frac{360}{320}$
$=270Hz$
Note When the speed of source and observer are much lesser than that of sound, the change in frequency becomes independent of the fact whether the source is moving or the observer.