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Question

The apparent frequency of the whistle of an engine changes by the ratio 5/3 as the engine passes a stationary observer. If the velocity of sound is 340 ms−1, then the velocity of the engine is

A
340 ms1
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B
170 ms1
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C
85 ms1
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D
42.5 ms1
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Solution

The correct option is D 85 ms1
Given : Velocity of sound vsound=340m/s
Let the frequency of the whistle be n and velocity of the engine be v.

Let the apparent frequencies heard by the observer be n and n′′ before and after the source passes the observer.

Doppler effect when source (S) approaches the stationary observer:

n=n[vsoundvsoundvsource] =n[340340v]

Doppler effect when source S moves away from the stationary observer:

n′′=n[vsoundvsound+vsource] =n[340340+v]

Now nn′′=53 (Given)

340+v340v=53

Thus v=85m/s

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