To understand the wave equation in a more physical way,
we need to remember a little algebra. Recall how the polynomial
could be factored into (*b*-*a*)(*b*+*a*)? We can do a similar
thing with the wave equation by rewriting it as a big operator
acting on *p*(*x*,*t*) as

and then factoring as

We see immediately that there are two operators acting on on *p*(*x*,*t*):

- , it turns out, represents
a forward going wave in the +
*x*direction, and - , it turns out, represents
a backward going wave in the -
*x*direction.

Tue Feb 25 21:24:33 EST 1997