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Doppler effect

  1. Feb 25, 2016 #1
    1. The problem statement, all variables and given/known data
    A guitar player is plucking a strong of length 30cm. How fast must the player move towards or away from the stationary observer, in order for the observer to mistake the fundamental frequency for the second harmonic?

    ANSWER: 2(Vsound) towards the observer

    2. Relevant equations
    Frequency for string fixed on both ends: f = 2n/vL
    Doppler effect for source moving towards stationary observer (observer will hear higher frequency):
    f" = vsound / vsound - Vsource

    3. The attempt at a solution
    f = 2n/vL = 2(1) / 343(0.3) = 205.8 Hz for the fundamental frequency --> set as f in the doppler equation
    f = 2(2) / 343(0.3) = 411.5Hz for the second harmonic --> set as f" in the doppler equation

    411.6 = 343 (205.8) / (343-vsound)
    Vsound = 171.5 m/s = 1/2 vsound

    I am getting 1/2 the speed of sound, rather than 2x the speed of sound which is the answer. What am I doing wrong?
     
  2. jcsd
  3. Feb 25, 2016 #2

    haruspex

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    Twice the speed of sound is clearly nonsense. The observer would not hear the player approach. Must be a typo.
    Your answer looks right.
     
  4. Feb 25, 2016 #3
    LOL thank you! My initial reaction to the "answer" was that it was an extremely hypothetical situation. Thanks for verifying!
     
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