# Lecture 4 - Physics 325 Lecture 20 Relativistic Doppler...

This preview shows pages 1–4. Sign up to view the full content.

Physics 325 Lecture 20 Relativistic Doppler Effect We begin with an observer at 90 ˚ . Non-relativistically, as we just saw, this observer sees no frequency shift. However, relativity tells us that the clock on the moving train is different than the clock with the stationary observer, so time-dilation slows the period of emitted waves according to τ γτ = (20.1) The wavelength and frequency shift accordingly: f f τ λ γ τ λ = = = (20.2) This is a purely relativistic effect. Now the rest of the argument goes very much like the train example above. Let’s repeat it with a moving source emitting light waves v G S’ S The source is at rest in the S’ frame and is emitting light waves. An observer measures them from the frame S. S’ moves with velocity v G with respect to S. If S’ were at rest with respect to S, then S would see a wave train of length c t in time t . However, since S’ is approaching S at speed v , the wave train gets shorter because the end of it is emitted closer to S by a distance v t , therefore the length of the wave train observed by S is x c t v t = ∆ − ∆ If the wave train consists of n full waves, we can write ( ) n c v λ t = (20.3) and the frequency is ( ) c cn f c v t λ = = (20.4)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document