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Doppletr effect ratio question

  1. Oct 23, 2012 #1
    1. The problem statement, all variables and given/known data

    A stationary detector measures the frequency of a sound source that first moves at constant velocity directly toward the detector and then (after passing the detector) directly away from it. The emitted frequency is f.

    During the approach the detected frequency is f'app and during the recession it is f'rec. If ( f'app - f'rec)/f = 0.741, what is the ratio vs /v of the speed of the source to the speed of sound?


    2. Relevant equations

    f ( f'app - f'rec)/f = 0.741

    f'app=f(v/(v+v(s) )

    f'rec=f(v/(v-v(s))

    3. The attempt at a solution

    (f(v/(v+v(s)))-(f(v/(v-v(s)))/(f) =0.741

    (v/(v+v(s)))-(v/(v-v(s)))=0.741

    (v(v-v(s))-v(v+v(s)))/((v+v(s))(v-v(s)) =0.741

    (-2V*V(s))/((v+v(s))(v-v(s)) =0.741

    Now I can't make the equation in the form V(s)/V no matter what I do. Where did I go wrong in this question?
     
  2. jcsd
  3. Oct 23, 2012 #2

    haruspex

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    Those equations would make f'app < f and f'rec > f. Does that seem right? Even swapping them, there's a problem with the v = vs case. Check with http://en.wikipedia.org/wiki/Doppler_effect.
     
  4. Oct 24, 2012 #3
    Never mind. I got the right answer. Assume v=1 . Solve for v(s) . You have your ratio.
     
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