Classical and Lorentzian transformation for doppler effect

  • #1
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?
 

Answers and Replies

  • #2
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Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 
  • #3
DEvens
Education Advisor
Gold Member
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What did I do wrong?

I think maybe you swapped f and f'.
 

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