lecture_4_07

lecture_4_07 - 05/07/09 Physics 13 - Fall 07 - G.R....

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Unformatted text preview: 05/07/09 Physics 13 - Fall 07 - G.R. Goldstein 1 Doppler Effect Source Receiver SOUND V S v sound V R f = v sound / λ in stationary frame (of air medium) Frequency at receiver: f = 1 + V R v sound 1- V S v sound f 05/07/09 Physics 13 - Fall 07 - G.R. Goldstein 2 Relativistic Doppler Effect - S Frame Receiver c V stationary source in S Light One pulse every T(sec) = 1 / f and λ = c/f. λ L 1st pulse at t=0 2nd pulse received before T since pulse goes shorter distance c t= ∆ λ- V t . So t = ∆ ∆ λ /(c+V) = 1 / [f(1+V/c)] and receiver is at x 2 =L - V t = L - V / [f(1+V/c)] ∆ 05/07/09 Physics 13 - Fall 07 - G.R. Goldstein 3 Relativistic Doppler Effect - Receiver • 2 events in S: E 1 : (L,0,0,0) and E 2 : (x 2 ,0,0,∆t) =(L-V∆t,0,0, ∆t) = (L-V/[f(1+V/c)], 0, 0, 1 / [f(1+V/c)]) • In S ′ (V approaching source): t 1 ′ = γ (t 1 + Vx 1 /c 2 ) = γ (VL/c 2 ) t 2 ′ = γ (t 2 + Vx 2 /c 2 ) = γ (∆t + V[L-V∆t] /c 2 ) = γ (VL/c 2 + ∆t[1 - V 2 /c 2 ]) rearranged = t 1 ′ + γ ∆t (1-V 2 /c 2 ) = t 1 ′ + ∆t / γ γ =1 / √ ( 1- V 2 /c 2 ) 05/07/09 Physics 13 - Fall 07 - G.R. Goldstein 4 Relativistic Doppler Effect - examples...
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This note was uploaded on 03/27/2008 for the course PHY 13 taught by Professor Garyr.goldstein during the Fall '04 term at Tufts.

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lecture_4_07 - 05/07/09 Physics 13 - Fall 07 - G.R....

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