Electromagnetic waves > Properties of emission and reflection of electromagnetic waves > Problem 12.1.5

Statement

$12.1.5.$ Two plane sinusoidal waves, each with amplitude $E_0$, have frequencies ω and $\omega + \Delta$, respectively, where $\Delta < \omega$, and propagate in the same direction, superimposing on each other. What is the maximum amplitude of the resultant wave? Determine the distribution of the average energy density of the resultant wave along the direction of propagation.

Solution

Answer

1. $E=2E_0;$

2. $\langle w \rangle = \frac{1}{2\pi} E_0^2 \cos^2 \left( \left( t - \frac{{z}}{2} \right) \frac{\Delta}{2} + \varphi \right).$