First slide

Doppler

Question

The apparent frequency of the whistle of an engine changes in the ratio 3 : 2 as the engine passes a stationary observer. If the velocity of sound is 30 m/s, the velocity of the engine is

Easy

A

33 m/s
B

44 m/s
C

66 m/s
D

55 m/s

Solution

$f_{1} = \frac{f_{0}}{(1 - \frac{V}{V_{S}})} and f_{2} = \frac{f_{0}}{(1 + \frac{V}{V_{S}})}$ where $V_{S} =$ Velocity of sound.
$∴ \frac{f_{1}}{f_{2}} = \frac{V + V_{S}}{V_{S} - V} \Rightarrow \frac{330 + V}{330 - V} = \frac{3}{2} \Rightarrow V = 66 m / s$

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