# Doppler Effect Equations

1. Jan 30, 2005

### bbfcfm2000

I know which equations to use for solving Doppler Effect problems, so figuring out which is the observer and which is the source and which is moving or stationary is not the problem, the problem I am having is in solving the actual formulas...... This question might belong in the math help section but I thought it was best to post this in the physics area because it does deal with a physics topic.

Anyway, I attached the equations as graphics (maybe somebody knows how to LATEX these?). I am looking for some help in rearranging these equations to solve for each of the variables, V,Vs,Vo,Fo,Fs.

Thanks!

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• ###### Doppler EQ - Moving Source.gif
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2. Jan 31, 2005

### Sirus

$$f_{o}=f_{s}\left({1\pm \frac{V_{o}}{V}}\right)$$

$$f_{o}=f_{s}\left({\frac{1}{1\pm \frac{V_{s}}{V}}}\right)$$

As I understand it, you are having trouble manipulating the equations to isolate certain variables. I suspect it is the plus-or-minus that is giving you trouble. Let's do an example. Let's isolate V in the first equation.

$$f_{o}=f_{s}\pm \frac{f_{s}V_{o}}{V}}$$
$$Vf_{o}=Vf_{s}\pm f_{s}V_{o}$$
$$Vf_{o}-Vf_{s}=\pm f_{s}V_{o}$$
$$V(f_{o}-f_{s})=\pm f_{s}V_{o}$$
$$V=\pm \frac{f_{s}V_{o}}{f_{o}-f_{s}}$$

Hope that helps. Keep in mind that if you encounter problems handling a $\pm$ sign, just separate the equation into the plus and minus forms, isolate the variable you wish in each equation normally, then unite the two final equations into one with a $\pm$. Think about what the symbol represents when dealing with it in your work.