hw4_p5405_f02 - z , show that Maxwells wave equation in...

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HW4 Phys5405 f02 due 10/8/02 1) JDJ 11-4 2) In O two evenly, but not exactly matched runners stand at (x,y,z) = (0,0,0) and (0,D,0), where D = 1 m. Starters with guns stand very close to each runner. The starter at y=0 fires his gun at t = 0 and at t = T = 2 × 10 - 8 s the starter at y = D fires his gun in order to even out the race. Observer O’ moves relative to this frame. The reference frames overlap and clocks are started at t=t’=0. a) Is is possible for O’ to see the guns fired simultaneously? If yes, find the velocity of O’ with respect to O. If not explain why not. b) Repeat for the case T = 0 . 2 × 10 - 8 . 3) Using the Lorentz transformation for O’ moving relative to O with velocity V = V e
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Unformatted text preview: z , show that Maxwells wave equation in vacuum has the same form for both O and O. Do not use the Lorentz invariance of the scalar product of two 4-vectors. 4) Let O move relative to O with velocity V . A laser at rest in O at the origin of Oemits light of frequency f that moves to the origin of O. Use the results for the Doppler eFect, derived in class, to show that the phase of the wave is a Lorentz invariant. That is show, k r- t = k r- t. rom this you deduce a new 4-vector ( k ,i /c). Here k = 2 / and f = /2 and f = c. 5) JDJ 11-5. Do the parallel case only. Make your e z direction coincide with V . 1...
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This note was uploaded on 12/24/2011 for the course PHYS 5406 taught by Professor Blecher during the Spring '10 term at Virginia Tech.

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