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Relativistic Doppler Effect and a Baseball

  • Thread starter TFM
  • Start date
  • #1
TFM
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[SOLVED] Relativistic Doppler Effect and a Baseball

Homework Statement



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?)

Homework Equations



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

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,

TFM

Edit: in the formulas, that should be a big Delta not a small Delta, Sorry
 

Answers and Replies

  • #2
275
2
If the DELf given is actually twice the doppler shift we're interested in... then what DELf should we use?
 
  • #3
TFM
1,026
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Would it be half?

TFM
 
  • #4
275
2
exactly
 
  • #5
TFM
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When I enter it into the equation, it just seems to spit out the speed of Light...?

TFM
 
  • #6
275
2
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?
 
  • #7
TFM
1,026
0
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:

TFM
 

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