Question

Consider the following two waves expressed in SI units: E_x=8sin(ky-ωt+π/2) and E_z=8sin(ky-ωt). Which wave leads, and by how much? Describe the resultant wave. What is the value of its amplitude?

Answer 1

1. The $E_x$ wave leads by $\pi/2$ , for it has addition term its phase.

2. The resultant wave is the following. We can write:$E_x = 8\sin(ky-\omega t+\pi/2) = 8\cos(ky-\omega t)$.

Thus, wave components are perpendicular to each other and the resultant wave has circular polarization. Then its magnitude:

$E = \sqrt{E_x^2 + E_z^2} = \sqrt{64\cos^2(ky-\omega t) +64\sin^2(ky-\omega t)} = 8.$