We are going to show that electromagnetic waves can propagate in a rectangular hollow metal tube. Let us consider that the perfectly conductive walls of the tube have length a on the x axis and b on the y axis, so that the waves propagate along the z axis. Let a> b, Supposed that the wave has the form Ē = (E,(z, v), E2(a, v), 0)e!(kz-wt) , (a) What is the dispersion relationship of the problem? (b) For a wave to be transmitted, k ^ 2 2 0 is needed. What is the minimum frequency for transmission? (c) Find the phase velocity and the group velocity of the solutions.

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We are going to show that electromagnetic waves can propagate in a rectangular hollow
metal tube. Let us consider that the perfectly conductive walls of the tube have length a on
the x axis and b on the y axis, so that the waves propagate along the z axis. Let a> b,
Supposed that the wave has the form
E = (E(z, v), E2(a, v), 0)e(kz-w) .
(a) What is the dispersion relationship of the problem?
(b) For a wave to be transmitted, k ^ 2 > 0 is needed. What is the minimum frequency for
transmission?
(c) Find the phase velocity and the group velocity of the solutions.
Transcribed Image Text:We are going to show that electromagnetic waves can propagate in a rectangular hollow metal tube. Let us consider that the perfectly conductive walls of the tube have length a on the x axis and b on the y axis, so that the waves propagate along the z axis. Let a> b, Supposed that the wave has the form E = (E(z, v), E2(a, v), 0)e(kz-w) . (a) What is the dispersion relationship of the problem? (b) For a wave to be transmitted, k ^ 2 > 0 is needed. What is the minimum frequency for transmission? (c) Find the phase velocity and the group velocity of the solutions.
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