# Doppler shift derivation from Lorentz Transformations

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1. Jan 29, 2017

### RyanP

1. The problem statement, all variables and given/known data
Show how one can obtain the Doppler transformation for the frequency of a receding
source just using the Lorentz transformations for the energy (where E=h).

2. Relevant equations
Relativistic transformations for momentum and energy:
E = γ(E' + vp'x)
pc/E = v/c = β

3. The attempt at a solution
E = γ(E' + vp'x)
since p = Eβ/c, E = γ(E' + Eβ2) = γE' (1+β2).

Which then would imply that = γ'(1+β2). But I have in my notes that the observed frequency = γ' (1-β). Where did I go wrong?

2. Jan 29, 2017

### vela

Staff Emeritus
The speed $\beta = \frac{pc}{E} = 1$ for electromagnetic radiation. It's not the same as $v$, the speed between the two reference frames.

3. Jan 29, 2017

### RyanP

That makes sense, thanks.