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Understanding Doppler Effect

  1. Dec 4, 2014 #1

    Waz

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    1. The problem statement, all variables and given/known data

    Two trumpet players are both playing with a pitch of 440 Hz, corresponding to the musical pitch A above middle C. However, one of the trumpet players is marching away from you so that your hear a beat frequency of 4 Hz from the two trumpets. With what speed is the departing trumpet player moving away from you? (The speed of sound in air is 340 m/s)

    2. Relevant equations

    f' = f(V+-Vo/V-+Vs)

    f2 - f1 = beat frequency

    3. The attempt at a solution

    How I approached the question was the following:

    f' = f(V/V+Vs)
    f(V/V+Vs) - f1 = beat

    so
    440(340/340+Vs) - 440 = 4
    which solves to Vs = 3.06 m/s

    However, looking at the answer (3.12 m/s) It seems I should have set the equation up as:

    440 - 440(340/340+Vs) = 4
    which goes to 3.119 m/s

    So conceptually speaking, how am I supposed to know how to set up the equation? Is it just what yields a positive answer? or is there something I'm not thinking of. I couldn't find anything specific online. Thanks for the help.
     
  2. jcsd
  3. Dec 5, 2014 #2
    How I thought of it is, the player is moving away, so the apparent frequency of the sound from his trumpet should be less than 440.
    We know that the difference, or lowering of the frequency, is 4Hz, so f' is 436.
    To have a frequency lower than the original, the denominator term of the velocity ratio should be greater. So we add the speed of air and the speed at which he is moving away.
     
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