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Doppler effect speed of sound

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  1. Oct 4, 2014 #1
    1. The problem statement, all variables and given/known data
    Problem: a car is moving away from a stationary observer at 25ms^-1. It emits a frequency of 810Hz and the observer hears an apparent frequency of 762Hz. What is the speed of sound in air at that time?

    2. Relevant equations
    The equation for a source moving away is

    f' = f(v/(v+us)) where us is speed of source.

    3. The attempt at a solution
    There are 2 v's and I need just one, I have no idea where to start, please can you help?
     
  2. jcsd
  3. Oct 4, 2014 #2

    Doc Al

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    Staff: Mentor

    Of the two speeds, one is given. Just solve for the other.
     
  4. Oct 4, 2014 #3
    Yes I know I have us but there are two v's in the equation and I don't know how to rearrange it to get one v on its own?
     
  5. Oct 4, 2014 #4

    Doc Al

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    Ah, so it's the algebra that's messing you up. First thing to do is get rid of that denominator on the right hand side. How can you do that?
     
  6. Oct 4, 2014 #5
    Multiply by it giving this?

    f'v+fus = fv
     
  7. Oct 4, 2014 #6

    Doc Al

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    Almost. That second term on the left should have an f', not an f.
     
  8. Oct 4, 2014 #7
    Oh yes, sorry.

    f'v + f'us = fv

    I still can't see how I set it down to just one v without somehow cancelling both out along the way?
     
  9. Oct 4, 2014 #8

    Doc Al

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    Keep the term with us where it is, but move all the others to the right. Then you can solve for us.
     
  10. Oct 4, 2014 #9
    But I'm solving for v?
     
  11. Oct 4, 2014 #10

    Doc Al

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    No, v is the speed of the car. You need to solve for us, which is the speed of sound.
     
  12. Oct 4, 2014 #11
    It's definitely v I need to find. According to my text book us is the moving source velocity. In the other equation it uses uo as moving observer velocity.
     
  13. Oct 4, 2014 #12

    Doc Al

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    You're right! (I must be losing my mind. Sorry about that!)

    So just collect all the terms with v in them to one side. Then you can isolate v. [Using ax + bx = (a+b)x]
     
  14. Oct 4, 2014 #13
    f'us=fv-f'v

    f'us =v(f-f')

    v=f'us/(f-f')

    Is that right?
     
  15. Oct 4, 2014 #14

    Doc Al

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    Perfect!
     
  16. Oct 4, 2014 #15
    Excellent! Thank you so much for your help! :)
     
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