Re: Tor

[brian whatcott <inet@INTELLISYS.NET>]

> [brian]
> > There are waves of many kinds. One that was not discussed
> > is the travelling wave that is excited in a stiff material by
> > applying a torque pulse. If I recall, this is non-dispersive.

At 18:53 1/28/00 -0500, Ludwik wrote:
> ...Is there any good reason for torsion waves (along a circular
> rod, or along a slinky) to be less dispersive than other stiff
> waves in the same medium(?)

The usual derivation compares the angle of twist and shear modulus
to density ratio of the torsionally excited travelling wave in a
torsionally stiff rod with the displacement and Young's modulus to
density ratio of a compression wave in an axially excited travelling
 wave.
(I note that 'stiffness' is a term that can represent
inverse compiance in several other modes as well as transverse
 deflection.)

 Because the models are similarly articulated, it is not surprising
 they predict comparable results.

   It is John D's flexural excitation that is different because it
is Euler's differential equation in a fourth power which rules,
and which determines the free transverse vibrations of a beam.

(Ref 1)

> Dispersion does prevent long range communication. Right?
> In fact, optical fibers would not work for long distances if
> the modulated light were not produced by a laser, or another
> highly monochromatic light sources.
> Ludwik Kowalski

Dispersion has been a problem in long range communication with
laser excited optical fibers. The Fourier analysis shows why
a narrow pulse has a stretched line width - to steal a concept
 from another thread on the list.

 One wishes to provide a high data rate, and a
light pulse washes out before too long unless measures are taken
to reduce dispersion. One way has been the graded fiber which
refracts peripheral rays towards the axis in a time locked fashion.

   But I find the distributed optical amplifiers exciting, in that
the need for extraordinary measures to reduce dispersion can be
avoided by regenerating the pulse train.

This evokes vivid memories of the relay repeaters provided for
early telegraphs - of  which so many were needed that these brass
bound objects are still available at relatively low cost.


Reference 1: Theory of Vibration with Applications, 2nd Ed
W.T. Thomson  Prentice-Hall

Brian




brian whatcott <inet@intellisys.net>
Altus OK