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*To*: AUDITORY@xxxxxxxxxxxxxxx*Subject*: Re: Wave reflection.*From*: "Richard F. Lyon" <DickLyon@xxxxxxx>*Date*: Thu, 10 Aug 2006 17:07:44 -0700*Comments*: To: reinifrosch@BLUEWIN.CH*Delivery-date*: Fri Aug 11 01:16:30 2006*In-reply-to*: <32679119.42451155234008083.JavaMail.webmail@lps3zhb.bluewin.ch>*References*: <32679119.42451155234008083.JavaMail.webmail@lps3zhb.bluewin.ch>*Reply-to*: "Richard F. Lyon" <DickLyon@xxxxxxx>*Sender*: AUDITORY Research in Auditory Perception <AUDITORY@xxxxxxxxxxxxxxx>

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

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 .

**References**:**Wave reflection.***From:*reinifrosch@xxxxxxxxxx

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