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Question

Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed of 1.0 ms1 and the man behind walks at a speed of 2.0 ms1. A third man is standing at a height 12 m above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency 1430 Hz. The speed of sound in air is 330 ms1. At the instant, when the moving men are 10 m apart, the stationary man is equidistant from them. The frequency of beats in Hz. heard by the stationary man at this instant, is ______

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Solution


Apparent frequency of A
fA=1430[3303302cosθ]=1430⎢ ⎢ ⎢112cosθ330⎥ ⎥ ⎥=1430[1+2cosθ330]

(By bionomial expansion)
Apparent frequency of B
fB=1430[330330+1cosθ]=1430[1cosθ330]

Then, the beat frequency of the system is given by,
Δf=fAfB=1430[3cosθ330]=13cosθ
=13(513)=5.00 Hz

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