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30 July, 02:45

A speaker fixed to a moving platform moves toward a wall, emitting a steady sound with a frequency of 235 Hz. A person on the platform right next to the speaker detects the sound waves reflected off the wall and those emitted by the speaker. How fast should the platform move, vp, for the person to detect a beat frequency of 4.00 Hz? Take the speed of sound to be 344 m/s.

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  1. 30 July, 03:00
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    Answer: 2.9 m/s

    Explanation:

    The frequency of the beat is 4 Hz

    The relative Doppler frequency is 235 + 4 = 239 Hz

    We would be solving this question, using the formula for Doppler's effect

    f (d) = f (v+vr) / (v-vs), where

    F = 235 Hz

    F (d) = 239 Hz

    v = 344 m/s and vr = vs

    239 = 235 (344 + vr) / (344 - vr)

    239 (344 - vr) = 235 (344 + vr)

    82216 - 239 vr = 80849 + 235 vr

    82216 - 80849 = 235 vr + 239 vr

    1376 = 474 vr

    vr = 1376/474

    vr = 2.9 m/s

    Thus the speed the platform should move is 2.9 m/s
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