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

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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)
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