Derivation of the Wave Equation

[wave eqn]

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:

[wave eqn]

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

Last updated Dec. 8, 1997.
Copyright George Watson, Univ. of Delaware, 1997.