9.1: Electromagnetic Waves in One Dimension
9.1.1 THE WAVE EQUATION
Before we start writing down how electromagnetic energy propagates in space as radiation, we'll dust off our mathematical background on waves. Thanks to Fourier analysis, we know that sinusoidal waves form a complete basis for all periodic functions, so we restrict our investigation to sinusoidal variations.
Suppose some quantity "" is propagating with speed in the direction, and we focus on sinusoidal "disturbances." At , And at any time
And if we look at a particular position (or other) and watch as a function of time, we'll see the same sinusoidal behavior
Generalizing to the 3-D case, instead of a wavenumber we have a wave vector
Any wave that looks like this satisfies the wave equation