### Derivation of the Wave Equation

Starting from the partial differential equation #1, differentiate once more with
respect to *z* in Step a.

Interchange the order of differentiation in Step b; we are only interested in solutions
which permit this!

Substitute partial differential equation #2 in Step c.

The wave equation results in Step d! Similar equations will result for the other components
of **E** and also for **B**. The general form of the wave equation in terms of
vector quantitites is:

Note that we started with two coupled first-order partial differential equations
and ended with an uncoupled second-order differential equation.

"http://www.physics.udel.edu/~watson/phys208/wave-eqn3.html"

Last updated Dec. 8, 1997.

Copyright George Watson, Univ. of Delaware, 1997.