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

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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

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66 m/s

33 m/s

55 m/s

44 m/s

answer is C.

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Detailed 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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