How can the Doppler equation be rearranged to solve for other variables?

[Zoey Brown]

Hi,
So i know that the doppler equation is as follos;

F(observed)= (Vsound + Vdetector) / (Vsound +- Vsource) x F(emitted)

Does anyone know how to reaarange the equation to solve for the other variables?

 

[QuantumCurt]

You can solve algebraically for any of the quantities that you want. It's best do this after clarifying what signs you will be using in the top and bottom.

$$f=\frac{v_s \pm v_d}{v_s \mp v_d}f_0$$

Suppose that your quantities tell you to put a plus in the numerator and a minus in the denominator. Then you get:

$$f=\frac{v_s +v_d}{v_s-v_d}f_0$$

Then you can solve algebraically for whatever variable you'd like. It's easier to do this after defining your sign conventions in most cases, but won't make a difference in all of them.

Are you trying to solve for a specific variable?

edit-by the way, it's conventional to use a lowercase $f$ to signify frequency. An uppercase $F$ typically represents force.