Assignment 3

Assignment 3 - 2. Electromagnetic waves (i.e. light)...

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PHYS-232 Heat and Waves - Homework 3 Winter Semester 2008 Due on Thursday, February 7, 2008 1. (a) Show that y ( x, t ) = Ae i ( kx - ωt ) + Be i ( kx + ωt ) (1) is also a solution of the wave equation for y , for c = ω/k . If you’ve dealt with complex variables a bit, you can convince yourself that this solution is actually equivalent to the trigonometric one you’re used to. Otherwise, note that e ix = cos x + i sin x with i = - 1. (b) Show explicitly that the sum of an incident wave of amplitude A and its (completely) re±ected wave are: y i + y r = 2 A sin( kx ) cos( ωt ) (2) and y i + y r = - 2 A sin( kx ) cos( ωt ) (3) For re±ection at a closed end and open end, respectively. Why is there a sign di²erence between solutions? (c) Prove that equation (2) is also a solution to the wave equation.
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Unformatted text preview: 2. Electromagnetic waves (i.e. light) traveling through a dielectric medium obey the wave equation, with c = 1 / . is the electric permittivity and is the magnetic permeability of the material. For water, = and = 1 . 77 . A light wave is traveling through water in the x direction, and hits an interface with a material with permittivity m and permeability m . What must the relation be between m and m such that there is no reection at the interface? 3. Solve problem 2.5.1 of the notes. 1...
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