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Re: Wave reflection.
Hi all,
This is very interesting stuff. I know a few of you gentlemen may wonder who I am, my name is Mark, I am a beginning college student that is interested in the basic cognitive mechanisms behind hearing internalization such as storage, processing, and retrieval. I am also interested in what grants the brain(Mine that I have noticed so far) the ability to apply (at will) environmental/modifying effects such as echo effects, octave adjustments, voice recognition/synthesis, etc. I have a keen interest in how the brain works at the cognitive level and have created a few "Functional block diagrams” of my own on how I interpret thought "I/O" using cognitive models of the brain as well as comparing them to the physical sub-processing areas.
This mailing list may be a bit advanced for me, so I have been mostly just reading these e-mails so that I would not say anything uneducated. But I am somewhat familiar with psychology and cognition. If you believe me to be misguided, I would be interested in pursuing further knowledge that perhaps you may be able to lead me too elsewhere. However, at times, I am able to relate to subject material such as the document mentioned below. I say these things, as I have received a notice requesting that I remove myself from this mailing list most likely for lack of contribution. Thanks for your time in advance,
Mark J.
----- Original Message -----
Sent: Thursday, August 10, 2006 8:07 PM
Subject: Re: Wave reflection.
If this WKB validity issue matters to you, you
better check out the appendix to Lloyd Watts's
JASA paper (L. Watts, "The Mode-Coupling
Liouville-Green Approximation for a
two-dimensional Cochlear Model", Journal of the
Acoustical Society of America, vol. 108, no. 5,
pp. 2266-2271, Nov., 2000), which you can find
linked here:
http://www.lloydwatts.com/cochlea.shtml
He says the usual criterion is only "first order"
correct, and that in fact the WKB solution
remains valid to much smaller k values (longer
wavelengths) than it suggests; so the long-wave
solution is OK near the base, where this
criterion says it should not be.
He also shows what goes wrong past resonance, and how to fix it.
Dick
At 8:20 PM +0200 8/10/06, reinifrosch@xxxxxxxxxx wrote:
>Hello again !
>
>I just found a good introductory treatment on nearly
>reflection-free waves, in the book "Physics of Waves"
>by W. C. Elmore and M. A. Heald (Dover, New York, 1969).
>In their section 9.1, they show that the WKB (Wentzel, Kramers,
>Brillouin) approximation is reflection-free, and that it is
>accurate if the local wavelength lambda obeys the following
>inequality:
>
>(d lambda / dx)^2 << 32 pi^2 . [their equation (9.1.15)]
>
>The corresponding inequality for the local wave number k is:
>
>k^-4 * (dk / dx)^2 << 8 .
>
>Reinhart Frosch.
>
>
>
>
>
>Reinhart Frosch,
>Dr. phil. nat.,
>r. PSI and ETH Zurich,
>Sommerhaldenstr. 5B,
>CH-5200 Brugg.
>Phone: 0041 56 441 77 72.
>Mobile: 0041 79 754 30 32.
>E-mail: reinifrosch@xxxxxxxxxx .