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Plane Wave Propagation

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Please see the attached file for a full description of the problem.

Consider a unit vector s = , and a plane perpendicular to s at a distance d from the origin.

a. For all points r within this plane, show that r.s = x sz + y sy + z sz = d.
b. Show that the scalar function f (x, y, z, t) = exp(i 2 pi (xsx + ysy + z sz)/L - nt)
represents a plane wave propagating along s with wavelength L and temporal frequency n, at a speed v = Ln

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r.s = ...

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