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AW: Re: Cochlear mechanics.
Hello Dick and List !
In the meantime, you have probably seen my
1.5-page text on the cochlear reflections;
nevertheless, I would like to react to your comments.
Datum: 25.08.2006 17:26
Betreff: Re: Cochlear mechanics.
>>S = S_0 * e^(-x/d) ,
>Reinhart, I think it would be more fair to call that a
>approximation more than an assumption. It's well known that for
>large enough d to get into a low-CF region, it decreases too
My present calculations are only about the basal
(i.e., high-charactaristic-frequency) region of the cochlea.
>>[...] 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
>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
>behaviour at low d.
The exciting property of "my" formula (i.e., N=4) is
that it reduces the left-hand side of the inequality
which if fulfilled guarantees accuracy of the WKB
(or LG) approximation and weakness of reflections
to zero !
>What do you mean by "even for low frequencies"? That was true of
>original function as well, right? So you just mean it doesn't
>up the no-reflections property?
In the case of the function S(x) = S_0 * e^(-x/d)
the mentioned inequality yields
d^-2 << 16 k^2 ;
Low frequency leads to low k and thus to a
violation of the inequality.
With best wishes,