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Re: Stiffness waves (was SLINKY)



Ludwik wrote:
... Here my dilemma. The stiffness wave satisfies the
differential wave equation, as demonstrated by John ....

John S. Denker replied:

Nope. If you re-read my derivation you'll see it explicitly applies
to ***longitudinal*** waves driven by compression. It isn't even
close to right for transverse waves driven by stiffness.

The condition for the validity of your derivation was Hooke's law,
the restoring force must be proportional to displacement. Is this not
true for an ideal transverse wave (small amplitude)?

You wrote:
More generally, we have that the extension of the tiny spring is
extension = (dy/dx) delta_x
and the force produced thereby is (using Hooke's law)
F(x) = -(dy/dx) delta_x / (s delta_x)
where
s = compliance per unit length.

What prevents me from applying the same to a transverse
displacement and from using k in Hooke's law (rather than s)?
I am assuming that there is no tension in a long string of tiny
masses connected by tiny relaxed springs.
Ludwik Kowalski