Re: A wave or not a wave ?

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

John Denker wrote:

> ... d) Standing waves are a red herring.  They can be considered
>  a fortuitous superposition of leftward plus rightward propagating
> waves.  In the space of all possible rightward and leftward wave
> patterns, standing waves are a subset of measure zero.
> Pedagogically speaking, I would not emphasize them and would
> not cite them as an example of typical waves.

Are you aware that in most elementary physics labs students are
introduced to waves via a vibrating string. On one side a vibrator,
on the other (about 2 m away) a pulley and the load to control
tension. Students try to create standing waves with different
number of loops by changing the load or frequency.

1) Do you think that this may be a source of misconceptions
    about waves?

2) If so then why is this experiment used nearly everywhere?

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