6. Let's derive the doppler effect for EM waves. Suppose that in frame S there is an electromagnetic wave described by E(x, y, z) = Eo cos(kx – wt) ŷ, B(x, y, z) = (Eo/c) cos(kx – wt) 2, where k=w/c. Another frame 5 is moving along the - direction at speed v relative to frame S. Show that the wave appears in frame S as E(x, y, z) = Eo cos(kx – wt) ŷ, B(x, y, z) = (Eo/c) cos(kx – wt) 2, and find the relations between E and Eº, k and k, and w and @. In particular, is the wave red- shifted (@w)?

6. Let's derive the doppler effect for EM waves. Suppose that in frame S there is an electromagnetic wave described by E(x, y, z) = Eo cos(kx – wt) ŷ, B(x, y, z) = (Eo/c) cos(kx – wt) 2, where k=w/c. Another frame 5 is moving along the - direction at speed v relative to frame S. Show that the wave appears in frame S as E(x, y, z) = Eo cos(kx – wt) ŷ, B(x, y, z) = (Eo/c) cos(kx – wt) 2, and find the relations between E and Eº, k and k, and w and @. In particular, is the wave red- shifted (@w)?