Q. The difference between the apparent frequency of a source of sound as perceived by the observer during its approach and recession is 2% of the natural frequency of the source. If the velocity of sound in air is $300ms^{- 1}$, the velocity of source is
A) $12ms^{- 1}$
B) $1.5ms^{- 1}$
C) $3ms^{- 1}$
D) $6ms^{- 1}$
Explanation
(c) When source is moving towards observer.
$n^{'} = \frac{vn}{v + v_{s}}$
When source is moving away from observer
$n^{''} = \frac{vn}{v - v_{s}}$
Now, $n^{'} - n^{''} = vn\left\lbrack \frac{v + v_{s} - v + v_{s}}{v^{2} - v_{s}^{2}} \right\rbrack = \frac{(2v_{s})vn}{v^{2} - v_{s}^{2}}$
When $v \gg v_{s},\ n^{'} - n^{''} = \frac{2v_{s}n}{v}$
Now $\frac{n^{'} - n^{''}}{n} = \frac{2}{100} = \frac{2v_{s}}{v} = \frac{2v_{s}}{300}$
$\therefore v_{s} = 3ms^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.