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Question

A source of sound is moving with a velocity of 50msâˆ’1 towards a stationary observer. The observer measures the frequency of sound as 500Hz. The apparent frequency of sound as heard by the observer when source is moving away from him with the same speed is (Speed of sound at room temperature 350msâˆ’1)

A
400Hz
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B
666Hz
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C
375Hz
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D
177.5Hz
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Solution

The correct option is D 375HzSpeed of sound, v=350 m/sSpeed of source, vs=50 m/sLet the original frequency of the source be fo.Apparent frequency heard by observer when a source moves towards the stationary observer :f′=fo[vv−vs]∴ 500=fo[350350−50] ⟹fo=428.6 HzApparent frequency heard by observer when a source moves away from the stationary observer :f′′=fo[vv+vs]∴ f′′=428.6[350350+50] =375 Hz

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