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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B
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C
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D
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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"=vv−vb×f
Frequency of the reflected waves as received by the moving motorist is f′"=v+vbv−vb×f′−v+vmv+vbf Therefore, the beat frequency is f′"=v+vmv−vb×f−v+vmv+vbf =2vb(v+vm)v2−v2bf