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Question on a doppler effect problem and equation

  1. Jul 10, 2011 #1
    1. The problem statement, all variables and given/known data
    Question: Two trains on separate tracks move toward one another. Train #1 has a speed of 130 km/hr and train #2 a speed of 90km/hr. Train 2 blows its horn, emitting a frequency of 500 Hz. What frequency is heard by the engineer on train #1?


    2. Relevant equations
    This is where I get stuck. Because this is a problem where two objects are moving towards each other their is no set equation according to my teacher. You have to "make one up" depending on the problem. So here are the equations I know.

    Source is moving and the observer is stationary:
    fo=fs(v/v-vs) For a source moving toward stationary observer. frequency goes up
    fo=fs(v/v+vs) For a source moving away from a stationary observer. frequency goes down

    Source is stationary and the observer is moving:
    fo=fs(1-vo/v) For a source moving away from a stationary source. frequency goes down
    fo=fs(1+vo/v) For a source moving toward a stationary source. frequency goes up

    I don't understand how to get equations for a problem where both objects are moving from these equations above.


    3. The attempt at a solution
    First I converted 130km/hr to m/s and got 36.1m/s. I did the same with the 90km/hr and got 25m/s.
    Vo=36.1m/s
    Vs=25m/s
    Fs=500Hz
    v=331
    Fo(train #1)=???

    I know all the terms I just don't know what equation to use.
     
  2. jcsd
  3. Jul 10, 2011 #2
    In these situations, this equation can be applied (proof might be a bit tricky though):

    [itex]f_{o}= f_{s} \large \frac{v \pm v_{o}}{v \pm v_{s}}[/itex]

    Where you would choose the signs of the basis of the convention you mentioned. For example, in your case, the numerator would be plus, and the denominator minus.
     
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