chp39_2 - PHY2061 R. D. Field Relativistic Doppler Shift...

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Unformatted text preview: PHY2061 R. D. Field Relativistic Doppler Shift (general case) y O-frame V r x Relativistic Doppler Shift! Consider an observer at rest in the O-frame and rr a light source moving with velocity β = V / c . Then the observed period, wavelength, and frequency are given by r ˆ T = γ (1 + β ⋅ r )T0 r ˆ λ = γ (1 + β ⋅ r )λ0 f0 r f= ˆ γ (1 + β ⋅ r ) r ˆ T = (1 + β ⋅ r )T0 r ˆ λ = (1 + β ⋅ r )λ0 f0 r f= ˆ (1 + β ⋅ r ) Classical Doppler Shift! rr 2 with β = V / c γ = 1 / 1 − β and where T0, λ0, and f0 are the period, wavelength, and frequency of the light in the frame at rest with the source. r ˆ Case I “away” ( β ⋅ r = 1 ): λaway = γ (1 + β )λ0 f away = f0 γ (1 + β ) r ˆ Case II “toward” ( β ⋅ r = −1 ): λtoward = γ (1 − β )λ0 f toward = f0 γ (1 − β ) r ˆ Case III “transverse” ( β ⋅ r = 0 ): λtransverse = γλ0 f transverse = f0 γ Transverse Doppler Shift! Department of Physics chp39_2.doc University of Florida ...
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This note was uploaded on 05/31/2011 for the course PHY 2061 taught by Professor Fry during the Spring '08 term at University of Florida.

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