Re: A wave or not a wave ?

[Bob Sciamanda <trebor@VELOCITY.NET>]

----- Original Message -----
From: "Ludwik Kowalski" <KowalskiL@MAIL.MONTCLAIR.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Sunday, July 02, 2000 3:03 PM
Subject: Re: A wave or not a wave ?


>  . . .
> Is it really necessary to define waves in "the most general
> mathematical way" when they are introduced for the first time.
> What is wrong with saying "many kinds of waves exist but
> TO BEGIN WITH we will limit our attention to harmonic
> waves"? That is good enough for ordinary acoustics, for
> explaining diffraction phenomena, for Fourier synthesis
> or analysis, etc. In other words, what is wrong with the
> traditional approach used in textbooks?
> Ludwik Kowalski

I always emphasize that it is useful to study harmonic oscillations and
waves as paradigms because of the work begun by Fourier.
I.E, harmonic functions can be used as a set of basis functions for
synthesizing a wide class of general functions.  (Draw an analogy to basis
vectors - this may be their first push into a profoundly important area of
mathematical physics.)

This approach does not limit the definition of waves (or oscillations);
it only offers a systematic method of attacking the general case - similar
to the use of unit vectors (divide and conquer?).

Bob

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor