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## Homework Statement

I have this Doppler effect formula, but I don't know how it was derived, I can't repeat the process myself to solve for speed of the source, I would really appreciate if someone could mathematicly solve this in steps, thank you very much.

## Homework Equations

[tex]f=f_{s}\frac{v}{v-v_{s}} \Rightarrow v_{s}=\frac{v(f-f_{s})}{f}[/tex]

## The Attempt at a Solution

I checked and this is the same thing as the equation above, but mine is messy and ugly, I don't know how to prepare "neaty" formulas like the one above, this often confuses me and forces me to do checks whether my formula is right or not.

[tex]v_{s}=\frac{-f_{s}v}{f}+v[/tex]

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