First slide

Doppler

Question

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 300 m/s, the velocity of the source is

Moderate

A

6 m/s
B

3 m/s
C

1.5 m/s
D

12 m/s

Solution

When the source is moving towards observer,
$n^{'} = (\frac{V}{V - V_{s}}) n$
When source is moving away from the observer
$n^{"} = (\frac{V}{V + V_{s}}) n n^{'} - n^{''} = \frac{V [2 v_{s}] n}{(v - v_{s}) (v + v_{s})} = \frac{V \times 2 v_{s} \times n}{v^{2} - v_{s}^{2}} When v >> v_{s}, then n^{'} - n^{''} = \frac{V \times 2 V_{S} \times n}{v^{2}} = \frac{2 v_{S}}{v} \times n Given that n^{'} - n^{''} = \frac{2}{100} \times n ∴ \frac{2}{100} \times n = \frac{2 v_{s}}{v} \times n v_{s} = \frac{v}{100} = \frac{300}{100} = 3 m / s$

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