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Re: SLINKY




Ludwik wrote:


I just discovered a misconception in my ways of thinking about
transverse waves. Am I the only one who was not aware of the
third kind of waves in a stretched spring? The textbooks I know
totally ignore contribution of stiffens to the speed of transverse
waves. And their "derivation" of the formula v=sqr(T/mu) is
nearly artificial (based on the centripetal force). I would not
accept the derivation without knowing that it happens to lead
to correct answer.


Ludwik must be at the same place in his course that I am. I
was planning on posting what I consider to be a swindel in
the derivation of energy propagation down the length of a
string for a harmonic transverse wave. My impression is that
the centripetal force derivation is uncommon in the calculus
level books I'm looking (as a side note, its the derivation I
use in class; I'll explain my thoughts later, I agree that it
is highly contrived).

I see most typical derivations for that rely on the small
angle approximation in order to replace sin (theta) with
tan(theta), this is done in order to use slope formulas. Now
bear in mind that this is a derviation for harmonic waves
whose wave forms are sinusoidal, and regardless of amplitude > there are
portions of the wave where the small angle
approximation is manifestly invalid!! Any comments?

BTW I use the centripetal force (despite its non-general
nature), for wave speed because it spirals back in a "neat"
fashion to two topice of the previous semester. Relative motion, and
centripetal force concepts.

Joel Rauber