# Homework Help: Relativistic Doppler Effect and a Baseball

1. May 8, 2008

### TFM

[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 $$f_0$$ and then measures the shift in frequency $$\Delta f$$ of the waves reflected from the moving baseball.

If the fractional frequency shift produced by a baseball is $$\frac{\Delta f}{f_0}$$ 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

$$u = \frac{c((\frac{\delta f}{f_0})^2) - 1}{\frac{\delta f}{f_0})^2 + 1}$$

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,

TFM

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

2. May 8, 2008

### lzkelley

If the DELf given is actually twice the doppler shift we're interested in... then what DELf should we use?

3. May 8, 2008

### TFM

Would it be half?

TFM

4. May 8, 2008

exactly

5. May 8, 2008

### TFM

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

TFM

6. May 8, 2008

### lzkelley

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. May 8, 2008

### TFM

I was using the wrong formula

The equation to use is:

$$\frac{\Delta f}{f_0} = \frac{u}{c}$$

Thanks for the assistance, lzkelley,

TFM