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Two Doppler shifts

  1. Apr 27, 2006 #1
    A stationary source directs an 800-Hz sound wave toward an approaching object moving with a speed of 25.0 m/s. What is the frequency shift of the reflected wave if the air temperature is 20ºC? (Hint: There are two Doppler shifts here. Why?)

    f = 800Hz
    the speed of sound = v = 331 + 0.6Tc = 343 m/s
    the speed of the object = vo = 25.0 m/s
    For the first doppler shift,
    f1 = (v + vo)/v * f
    f1 = 858 Hz
    For the second doppler shift, I'm guessing that we use the object moving as the source of the sound and the original sound source as the observer:
    f2 = v/(v - vo) * f1
    f2 = 925 Hz

    But the answer is 126 Hz!:confused:
  2. jcsd
  3. Apr 28, 2006 #2


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    The shift in frequency is the difference between the final frequency and the initial one, so your answer is actually correct. (925 - 800 = 125 Hz, which is close enough to the expected answer).
  4. Apr 28, 2006 #3


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    the Google calculator says:
    (((343 + 25) / (343 - 25)) * 800) - 800 = 125.786164
    Sometimes it's best to get an algebraic answer in terms of the given variables, then plug in the numbers. Otherwise, intermediate numerical values can introduce round-off errors.
  5. Apr 28, 2006 #4
    Yeah, my value of 125 Hz comes from the fact that I used f1 = 858 Hz, when I think it should've been 858.3xxxxxxx.... I get it now. Thanks.
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