First slide

Doppler

Question

The difference between the apparent frequency of a source of sound as perceived by an observer during its approach and recession is 2% of the natural frequency of the source. lf the velocity of sound in air is 300 m/sec, the velocity of the source is (It is given that velocity of source << velocity of sound)

Moderate

A

6 m/sec
B

3 m/sec
C

1.5 m/sec
D

12 m/sec

Solution

When the source approaches the observer
Apparent frequency $n^{'} = \frac{v}{v - v_{s}} . n = n [\frac{1}{1 - \frac{v_{s}}{v}}]$
= $n {[1 - \frac{v_{s}}{v}]}^{1} = n [1 + \frac{v_{s}}{v}]$
(Neglecting higher powers because $v_{s} < < v$ )
When the source recedes the observed apparent frequency
$n^{"} = n [1 - \frac{v_{s}}{v}]$
Given $n^{'} - n " = \frac{2}{100} n, v = 300 m / \sec$
$∴ \frac{2}{100} n = n [1 + \frac{v_{s}}{v}] - n [1 - \frac{v_{s}}{v}] = n [2 \frac{v_{s}}{v}]$
$\Rightarrow \frac{2}{100} = 2 \frac{v_{s}}{v} \Rightarrow v_{s} = \frac{v}{100} = \frac{300}{100} = 3 m / \sec$

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