Re: linearity of mechanical coupling

Robert Adams wrote:
On Apr 3, 9:18 pm, Jerry Avins <j...@xxxxxxxx> wrote:
Robert Adams wrote:
This question might better be posed on an acoustics group, but my
guess is that someone here will know the answer.
I have been told by knowledgeable acoustics people that when a sound
wave travels through a solid rather than air, the speed of propagation
varies with the frequency (I believe acoustics folks talk about
"bending" as the mechanicsm for propagation). To me this means that if
I mix 2 frequencies together and couple them into a solid, the phase
relationship between the two frequencies will vary as I move my pickup
point along the surfacfe of the solid.
My question is this; does the statement that the speed of propogation
is frequency-dependant also imply non-linearity, and therefore have I
generated new frequencies when I mix several frequencies together? Do
I get distortion with only a single frequency excitation?
If it is non-linear, assuming that I knew the relationship between the
propagation speed and the frequency (for single frequencies), how
would I characterize such a system mathematically?
Propagation velocity being a function of wavelength is called
"dispersion" whether in optics or acoustics. Snell's law applies in
either case. Acoustic lens structures exist and have been used to focus
and disperse sounds. Non-linearity, if involved at all, is a side effect
and not fundamental to the phenomenon.

Jerry
--
Engineering is the art of making what you want from things you can get.
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- Show quoted text -



My problem is that if I think of a linear mechanical system, I should
be able to define a spatial R-L-C lumped approximation, and once I
have done that I don't see how propagation speed could depend on
wavelength (propagation speed in not the same as group delay at a
given spatial point; I am assuming no effects from rolloffs, the
system is flat at all frequencies that are injected). Try to think of
a R-L-C transmission line model where the propogation speed varies
with frequency; I can't think of how this could happen in a linear
system.

Dispersion occurs on transmission lines also. They can be modeled (below some critical frequency) with R-L-C components and no others. Instead of my writing a treatise on transmission lines, try Google. Start with http://www.ece.uci.edu/docs/hspice/hspice_2001_2-269.html

Waveguides are also dispersive. Unlike with transmission lines, it is not even theoretically possible to avoid it. All optical fibers show dispersion. The propagation velocity is the inverse of the refractive index, and refractive index is a function of wavelength. No distortion is involved.

Jerry
--
Engineering is the art of making what you want from things you can get.
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