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*To*: AUDITORY@xxxxxxxxxxxxxxx*Subject*: Re: Cochlear mechanics.*From*: "Richard F. Lyon" <DickLyon@xxxxxxx>*Date*: Fri, 25 Aug 2006 08:26:39 -0700*Comments*: To: reinifrosch@BLUEWIN.CH*Delivery-date*: Fri Aug 25 11:52:39 2006*In-reply-to*: <24823985.104801156507713491.JavaMail.webmail@lps10zhh.bluewin.ch>*References*: <24823985.104801156507713491.JavaMail.webmail@lps10zhh.bluewin.ch>*Reply-to*: "Richard F. Lyon" <DickLyon@xxxxxxx>*Sender*: AUDITORY Research in Auditory Perception <AUDITORY@xxxxxxxxxxxxxxx>

Dear colleagues,

In models of the basal region of the cochlea, the basilar- membrane stiffness S is often assumed to depend on the longitudinal coordinate x as follows:

S = S_0 * e^(-x/d) ,

Reinhart, I think it would be more fair to call that a convenient approximation more than an assumption. It's well known that for large enough d to get into a low-CF region, it decreases too slowly.

where d is about 3 mm. Yesterday I found that absence of significant reflections is predicted even for low frequencies if a different function is used instead:

S = S_0 * [1 - x/(4d)]^4 .

The use of [1 - x/N]^N as an approximation for exp(-x) is often very useful, for example in approximating Gaussians or high powers of cosines, in my experience, but I had not looked at it in this particular application. It looks like a useful way to get the stiffness and CF to go to 0 for finite d while preserving the desired behaviour at low d.

I have written a text-file of about 1.5 pages giving details. Please write if you want to receive that file.

Definitely would love to see it.

Thanks.

Dick

With many thanks, sincerely,

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**:**Cochlear mechanics.***From:*reinifrosch@xxxxxxxxxx

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