You are standing beneath a Ferris wheel when two children riding in cars on oppo

Question

You are standing beneath a Ferris wheel when two children riding in cars on opposite sides of the wheel both scream at 580 Hz . Your well-trained ears notice a beat frequency that is maximum when one child is moving directly toward you and the other is moving directly away from you. The Ferris wheel takes 24.0 s to complete one rotation, and its diameter is 23.0 m . You begin to wonder whether a Doppler shift could produce observable beats under these circumstances.

Part A:- Determine the beat frequency. Express your answer with the appropriate units.

Explanation / Answer

Speed of ferris wheel will be

V = w*r

w = 2*pi/T

V = 2*pi*r/T

V = 2*pi*11.5/24 = 3.01 m/sec

Now beat frequency will be

dF = f1 - f2

f1 = frequency when boy is moving towards stationary object

f1 = f0*V/(V - Vs)

f1 = frequency when boy is moving away from stationary object

f1 = f0*V/(V + Vs)

dF = f0*V/(V - Vs) - f0*V/(V + Vs)

Using given values:

dF = 580*343*[1/(343 - 3.01) - 1/(343 + 3.01)]

dF = 10.18 Hz

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