Classical and Lorentzian transformation for doppler effect

[leandrofosque]

Hi everyone, I am having some problems understanding Bergmann's problems.

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?

 

[DEvens]

What did I do wrong?

I think maybe you swapped f and f'.