3.1 E_x = E_o cos(omega t - kz + phi_o), where: E_x = electric field along x at

Question

3.1

E_x = E_o cos(omega t - kz + phi_o), where: E_x = electric field along x at position z at time t. k = propagation constant, or wavenumber = 2 pi/lambda, lambda = wavelength, omega = angular frequency, E_o = amplitude of the wave, phi_o is a phase constant which accounts for the fact that at t = 0 and z = 0 E_x may or may not necessarily be zero depending on the choice of origin. (omega t - kz + phi_o) = phi = phase of the wave. This equation describes a monochromatic plane wave of infinite extent traveling in the positive z direction. To Do: For integer values of z from 1 to 10, 0 phase, and (omega x t) = 2pi, plot Ex. Write an equation for a wave propagating in the negative z direction. You add two waves with phase difference 180 degree, what is the result? You add two waves with phase difference 2pi radians, what is the result?

Explanation / Answer

1) Ex is a sinusoidal curve , with maximum value of Eo and minimum value of - Eo .

2) wave propagating in -ve Z direction

=> Ex = Eo * cos(wt + kz + phi)

3) This will give rise to a standing wave .

4) The resulting wave will be same as original wave with double the amplitude (2Eo) .

=>   Ex = 2Eo * cos(wt - kz + phi)

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