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Question

A band playing music at frequency f is moving towards a wall at a speed vb. A motorist is following the band with a speed vm. If v is the speed of sound, the expression for the beat frequency heard by the motorist is

A
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Solution

The correct option is C
The motorist receives two sound waves: direct one and that reflected from the wall.
f=v+vmv+vbf
For reflected sound waves:
Frequency of sound wave reflected from the wall is
f"=vvvb×f

Frequency of the reflected waves as received by the moving motorist is
f"=v+vbvvb×fv+vmv+vbf
Therefore, the beat frequency is
f"=v+vmvvb×fv+vmv+vbf
=2vb(v+vm)v2v2bf

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