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Correction to my posting of Oct. 17.

Hello Dick Lyon, Matt Flax, and List,

I shall answer your messages shortly; but before that I want to 
correct a mistake in my long posting of October 17.

Under point 4 I discussed Fig. 3 of de Boer and Nuttall (1999), 
"The 'inverse problem' solved ...", JASA 105, 3410-3420. About 14 
lines before the end of my message, I claimed that extrapolation 
yields a resonance frequency of 16.8 kHz for a "BM-resonator" at a 
position of x_b = 7.8 mm. After having sent off my posting, I 
realized that the unusual abscissa scale used in the lower panel 
(linear between -1 and +1, logarithmic otherwise) falsifies 
straightforward extrapolation. I then replotted the short-dashed line 
(labelled "imag. part") in the lower panel using ordinary linear 
scales for both coordinate axes. Now the extrapolation yielded that 
the imaginary part of the BM impedance vanishes not at 130 percent = 
7.8 mm, but rather already at about 105 percent = 6.3 mm. 

The reason why the resonance frequency of the BM-resonator (spring 
= BM-fibers, mass = organ of Corti) occurs at the zero of the 
imaginary part of the BM-impedance (across-BM pressure difference 
divided by BM velocity) is given, e.g., in Section 3.2 of de Boers 
Chapter in the book "The Cochlea" (Springer, 1996).

So for the "panoramic view" adopted in this Fig. 3 [fixed sine-tone 
frequency (16.8 kHz) and level (20 dB), and variable location on BM 
(x_b = 0 to 6 mm) the "snapshot" of the travelling wave shows a hint 
of the passive response peak at about x_b = 3.6 mm (that peak would 
also be observed post mortem, i.e., without viable OHC's), and an 
active peak at x_b = 5.0 mm. The wave reaches only up to x_b = 6 mm, 
and thus does not attain the BM-resonator (located at x_b = 6.3 mm) 
the resonance frequency of which is equal to the considered sine-wave 
frequency of 16.8 kHz.

The guinea-pig BM is about 19 mm long, and guinea pigs hear well 
sine-tones from 0.2 to 45 kHz. Taking into acount the observed 
function of active-peak location versus sine-tone frequency, I 
estimate that in the BM-region of this Fig. 3 one octave corresponds 
to about delta-x_b =  2.7 mm. Therefore it could be said (sometimes 
confusingly) that the just mentioned three locations (3.6, 5.0, and 
6.3 mm) are separated by half-octaves.

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 .

----UrsprÃngliche Nachricht----
Von: DickLyon@xxxxxxx
Datum: 18.10.2007 02:38
An: <reinifrosch@xxxxxxxxxx>, <AUDITORY@xxxxxxxxxxxxxxx>
Betreff: Re: AW: Cochlea Amplifier models : a new list


I remain unclear on the point of your long note, interesting though 
it was.
Are you saying that the passive peak and the active peak that are a 
octave apart in cochlear mechanics are distinct things, or are you 
that they are two ends of a level-dependent continuum?  I tend to 
the latter; do the data you describe tend to push the 
interpretation one
way or the other?