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Problem 3 from Chapter 4 from Intro to the Theory of Relativity by Bergmann

1. Suppose that the frequency at a light ray is f with respect to a frame of reference S. Its frequency f′ in another frame of reference, S', depends on the angle α between the direction of the light ray and the direction of relative motion of S and S'. Derive both the classical and the relativistic equations stating how f' depends on f and the angle α. The light may be treated as a plane scalar wave moving with velocity c.

Sol: classical ##f'= f(1-(v/c)cosα) ##

relativistic ##f'= γ. (classical) ##(where γ is the Lorentz factor)

What I did:

## x=ctCosα## , then ##x=fλtCosα##

From Galilean transf. we have: ##x=x'-vt ,##

then ##fλtCosα= f'λtCosα-vt , f = f' - \frac{v}{λCosα}, f = f' - (\frac{vf'}{cCosα})##

What did I do wrong?