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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.
Dr. phil. nat.,
r. PSI and ETH Zurich,
Phone: 0041 56 441 77 72.
Mobile: 0041 79 754 30 32.
E-mail: reinifrosch@xxxxxxxxxx .
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
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
way or the other?