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Relativistic Doppler Effect and a Baseball

  1. May 8, 2008 #1


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    [SOLVED] Relativistic Doppler Effect and a Baseball

    1. The problem statement, all variables and given/known data

    A baseball coach uses a radar device to measure the speed of an approaching pitched baseball. This device sends out electromagnetic waves with frequency [tex] f_0 [/tex] and then measures the shift in frequency [tex] \Delta f [/tex] of the waves reflected from the moving baseball.

    If the fractional frequency shift produced by a baseball is [tex]\frac{\Delta f}{f_0}[/tex] 2.88×10−7, what is the baseball's speed? (Hint: Are the waves Doppler-shifted a second time when reflected off the ball?)

    2. Relevant equations

    [tex] u = \frac{c((\frac{\delta f}{f_0})^2) - 1}{\frac{\delta f}{f_0})^2 + 1} [/tex]

    3. The attempt at a solution

    I tried putting the variables in, but becasue there is a double doppler shift, the asnwer was incorrect. Was is the best way to do this question when a Double Shift occurs?

    Any ideas gratly appreciated,


    Edit: in the formulas, that should be a big Delta not a small Delta, Sorry
  2. jcsd
  3. May 8, 2008 #2
    If the DELf given is actually twice the doppler shift we're interested in... then what DELf should we use?
  4. May 8, 2008 #3


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    Would it be half?

  5. May 8, 2008 #4
  6. May 8, 2008 #5


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    When I enter it into the equation, it just seems to spit out the speed of Light...?

  7. May 8, 2008 #6
    You're equation might not be quite right...

    namely: where you have Delf / f; i think it should be (observed f) / (source f).
    Del f / f = (source f - observed f) / (source f)

    .. try it the other?
  8. May 8, 2008 #7


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    I was using the wrong formula :bugeye:

    The equation to use is:

    [tex] \frac{\Delta f}{f_0} = \frac{u}{c} [/tex]

    Thanks for the assistance, lzkelley, :smile:

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