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Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed of 1.0ms1 and the man behind walks at a speed of 2.0ms1. A third man is standing at a height 12m 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 1430Hz. The speed of sound in air is 330ms1. At the instant. when the moving men are 10m 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]
Δf=fA=fB=1430[3cosθ330]=13cosθ
=13(513)=5.00Hz
828507_904043_ans_0e9dc1d69a354092927c7c70ae4aff7c.png

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