A woman stands at rest in front of a large, smooth wall. She holds a vibrating t

Question

A woman stands at rest in front of a large, smooth wall. She holds a vibrating tuning fork of frequency f_0 directly in front of her (between her and the wall). She now runs toward the wall with a speed v_W. She detects beats due to the interference between the sound waves reaching her directly from the fork and those reaching her after being reflected from the wall. How many beats per second will she detect? (Note: If the beat frequency is too large, the woman may have to use some instrumentation other than her ears to detect and count the beats.) Use v for the speed of sound. Express your answer in terms of the given quantities. If she instead runs away from the wall, holding the tuning fork at her back so it is between her and the wall, how many beats per second will she detect? Use v for the speed of sound. Express your answer in terms of the given quantities.

Explanation / Answer

frequency of tunning fork is f_o when both source and observer approach each other the apparent frequency f = f_o [ V - V_o / V +V _s ] where V is speed of light V_o velocity of observer V_ s velocity of source number of beats n = f _ o - f = f _o - f_o [ V - V_o / V + V _s ] = f_o [ V_o +V_s / V + V _s ] b)If she instead runs away from the wall apperent frequency f = f_o [ V + V_o / V - V _s ] number of beats n ' = f_o - f_o [ V + V_o / V - V _s ] = f_o [ V_o - V_s / V - V _s ]

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