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Question

A whistle of frequency 540 Hz is moving in a circle of radius 2 ft at a constant angular speed of 15 rad/s. What are the lowest and highest frequencies heard by a listener standing at rest, a long distance away from the centre of the circle?
(velocity of sound in air is 1100 ft/sec.)

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Solution

As the whistle is moving along a circular path let its angular velocity be ω
Therefore Iinear velocity
vs=ωR=2×15=30ft/s
At points A and B, the velocity vs of whistle is parallel to line OP; i.e. with respect to observer at P, whistle has maximum velocity vs away from P at point A, and towards P at point B. (Since distance OP is large compared to radius R, whistle may be assumed to be moving along line OP)
Observer, therefore, listens maximum frequency when source is at B moving towards observer:
fmax=vvvsf=1100110030×540=555Hz
minimum frequency when source is at A moving away from the observer
fmin=vv+vsf=11001130×540=525Hz

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