Re: definition of "wave"

[John Denker <jsd@MONMOUTH.COM>]

At 05:49 PM 1/26/00 -0500, Ludwik Kowalski wrote:
>
> Can somebody bring an acceptable general definition of a wave
> for classical physics?

The usual pat answer is:
        A wave is a disturbance that propagates leaving the
        medium (if any) behind.

> My impression was (up to now) that all waves
> (by definition ?) must satisfy the familiar second order
> derivative equation.

Nope.  There's lots of different waves and wave equations...
  -- some have significant nonlinearity, some don't;
  -- some have significant dispersion, some don't;
  -- some have significant damping, some don't.

Example:  Solitons and shock waves are highly nonlinear, but they're
perfectly good waves.  They're propagating disturbances.

Example:  People pay good money for highly dispersive media such as
diamonds and lead crystal.  Waves in dispersive media are perfectly good waves.

Example:  The most familiar waves of all, waves on the surface of a pond,
are damped, nonlinear, and dispersive.  You wouldn't want to define them
out of existence.

-------

Further discussion of some marginal cases:

(a) Standing waves are not exactly *propagating* disturbances, but still I
call them waves.

(b) Evanescent waves are an even more troublesome case.  They don't really
propagate, either, but still I want to call them waves.

(c) I do _not_ like to use the word "wave" to describe solutions to the
diffusion equation.  The don't propagate very well, but that doesn't settle
the issue, because of the previous two examples.  Sigh.  I suppose one
could consider them to be grossly overdamped waves, but that seems like
stretching a point.

I guess (a) and (b) sneak into the wave category because they are solutions
to an equation which given slightly different initial conditions would
yield freely propagating solutions.