Chapter1_19 - − = ⋅ r ˆ r 1 1 1 1 1 1 f f f toward...

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PHY3063 R. D. Field Department of Physics Chapter1_19.doc University of Florida Relativistic Doppler Shift ( general case ) Consider an observer at rest in the O-frame and a light source moving with velocity c V / r r = β . Then the observed period, wavelength, and frequency are given by ) ˆ 1 ( ) ˆ 1 ( ) ˆ 1 ( 0 0 0 r f f r T r T + = + = + = β γ λ β γ λ β γ r r r ) ˆ 1 ( ) ˆ 1 ( ) ˆ 1 ( 0 0 0 r f f r T r T + = + = + = β λ β λ β r r r with 2 1 / 1 / β γ β = = c V r r and where T 0 , λ 0 , and f 0 are the period, wavelength, and frequency of the light in the frame at rest with the source. Case I “away” ( β β = r ˆ r ): 0 0 0 0 1 1 ) 1 ( 1 1 ) 1 ( f f
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Unformatted text preview: − = ⋅ r ˆ r ): 1 1 ) 1 ( 1 1 ) 1 ( f f f toward toward − + = − = + − = − = Case III “transverse” ( ˆ = ⋅ r r ): γλ f f transverse transverse = = y x V O-frame r Relativistic Doppler Shift! Classical Doppler Shift ( β << 1)! Transverse Doppler Shift!...
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