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hw4_p5405_f02

# hw4_p5405_f02 - z show that Maxwell’s 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 Maxwell’s 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 O’emits 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’-ω ’t’ = k · r-ω t. ±rom this you deduce a new 4-vector ( k ,i ω /c). Here k = 2 π / λ and f = ω /2 π and f λ = c. 5) JDJ 11-5. Do the parallel case only. Make your e z direction coincide with V . 1...
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