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Re: Cochlear mechanics.
At 12:08 PM +0000 8/25/06, reinifrosch@xxxxxxxxxx wrote:
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.
What do you mean by "even for low frequencies"? That was true of the
original function as well, right? So you just mean it doesn't mess
up the no-reflections property?
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.
With many thanks, sincerely,
Dr. phil. nat.,
r. PSI and ETH Zurich,
Phone: 0041 56 441 77 72.
Mobile: 0041 79 754 30 32.
E-mail: reinifrosch@xxxxxxxxxx .