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Doppler shift with 2 trombones

  1. Aug 5, 2013 #1
    1. The problem statement, all variables and given/known data

    Mary is blowing her trombone at 400hz.

    Paul is approaching her at speed v, blowing the same type of trombone. These trombones has a maximum frequency of 500hz. What is the maximum speed Paul can approach Mary, and still cancel out her trombone noise?

    2. Relevant equations

    f = f0/(1-vs/v)

    Speed of sound = 340m/s

    3. The attempt at a solution

    Max freq 500, so:

    500 = 400/(1-v/340)

    Solving for v, I get 68 m/s. The answer is 85 m/s. What's going on?
     
  2. jcsd
  3. Aug 5, 2013 #2

    Zondrina

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    I don't think your equation is correct. Why are you saying the velocity v is equal to the speed of sound in the air?
     
    Last edited: Aug 5, 2013
  4. Aug 5, 2013 #3
    The perceived frequency is equal to the real frequency divided by (1-v(speed of approaching source)/v(speed of sound)). Is that the wrong formula?
     
  5. Aug 5, 2013 #4

    Zondrina

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    No that's not what I'm saying. This is indeed 100% correct after dividing through by v :

    ##f = \frac{f_0}{1 - \frac{v_s}{v}}##

    I meant why are you using ##v = 340 m/s## in your calculation, it doesn't make any sense.

     
  6. Aug 5, 2013 #5
    Pauls speed divided by the speed of sound... What's wrong with dividing by 340?
     
  7. Aug 5, 2013 #6

    haruspex

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    I agree with your calculations and answer of 68 m/s. 85 m/s is the answer if the question is how fast do you have to move away from a source of 500/s to hear it as 400/s.
    Zondrina, you seem to be confused by the fact that the formula quoted uses vs for the speed of the source and v for the speed of sound, whereas in the question v stands for the speed of the source.
     
  8. Aug 5, 2013 #7

    Zondrina

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    So Paul is coming at Mary at mach 1? I think you mean Paul comes at Mary with a speed of ##v_s## right :)?

    As for your question though, I think you have worded it incorrectly, left information out or the answer is a typo.

    If Paul is going away from Mary, then the answer of 85 m/s makes sense. ##f## is the apparent frequency and you said Mary plays the trombone at 400Hz. Hence ##f = 400 Hz## and so we can also say ##f_0 = 500 Hz##. Then you get :

    400 = 500/(1 - (v/340))
    v = 85 m/s

    EDIT : I'm not confused harup, I just believe he didn't put any effort into typing out the question properly.
     
    Last edited: Aug 5, 2013
  9. Aug 5, 2013 #8

    haruspex

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    Seems to me Gauss MD stated the question as given to him/her, and stated a formula in a reasonably standard form (though it is better to state what all the variables represent when quoting a formula). There should be no expectation that the two agree on allocation of symbols to entities.
     
  10. Aug 5, 2013 #9

    Zondrina

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    Yes I agree I suppose, I'm just picky about notation IMO. I think information can get lost in translation through a problem if there isn't any consistency.
     
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