Re: SLINKY

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

Ludwik Kowalski wrote:

> ... But, as you "proved", to predict the longitudinal speed we
> simply replace T by s, the spring stiffness (which appears in
> Hookes law for flexion).

I should have said the "s, the spring compliance". The word "proved"
was quoted to emphasize what you wrote yesterday about differences
between proving things in math and in science. Your derivation is
general enough to apply to both longitudinal and transverse speeds.
Bringing torsional disturbances would not be appropriate for a one
dimensional approximation (but you are correct, it can be used for
a real slinky).

I am puzzled by the fact that the derived formula, v=sqr(k/mu),
for the transverse speed does not agree with v=sqr(T/mu), which
students often test in physics labs (via standing waves). Why should
a spring disturbance propagate at a different speed than a string
disturbance when T and mu are exactly the same? Next time I do
the class demo with the long spring I will try to see which of the
two formula is in agreement with reality.
Ludwik Kowalski