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Doppler Effect and Wind Speed

  1. May 8, 2010 #1
    1. The problem statement, all variables and given/known data
    Two jet airplanes are flying due east. The leading jet is flying at 1.3 times the speed of sound. The trailing jet is flying at 464 mph (both relative to the ground). The wind is blowing 182 mph due west. If the engine of the leading jet has a frequency of 2824 Hz, what frequency is heard by the pilot of the trailing jet? The speed of sound is 607 mph at this altitude.
    Answer in units of Hz.

    2. Relevant equations
    f' = f [(1+Vo/V) / (1+Vs/V)]

    3. The attempt at a solution

    First, I converted everything to SI units:
    Jet 1: 1.3(Speed of Sound Given) = 1.3(607) = 789.1 mph = 352.759 m/s
    Jet 2: 464mph = 207.427 m/s
    Sound: 607mph = 271.353 m/s
    Wind: 182mph = 81.361 m/s
    Frequency: 2824Hz

    I honestly have no idea how to incorporate wind into this problem. We've gone over similar problems in class, but they have always been under conditions where the wind speed isn't given or is "negligible."
    I figured because the wind is blowing due west, the perceived "motion" of the sound waves, and because it was actually motion of the medium, I could simply add the wind speed to the speed of sound:
    81.361 + 271.353 = 352.714 m/s

    After doing this, I solved the problem as I would normally:

    f' = 2824 [( 1 + (207.427/352.714)) / (1 + (352.759/352.714))] = 5648.36Hz

    However, this is incorrect. I am almost sure I went wrong with factoring in the wind speed, but I haven't been able to find any information regarding this. Please help!
  2. jcsd
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