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Re: mechanical cochlear model [Q.2]

Dear Reinhart:

You say that in the TW model, the lowest resonance frequency "may well be"
considerably greater than 20 Hz. That sounds like lawyer-speak to me.

The TW might be able to explain cochlear responses from 20 kHz down to,
say, 500 Hz? As a scientist with an interest in rigor, is that good
enough? We CAN hear 20 Hz. How?

Your concession to physical reality seems like another little death for
the TW theory.

At the same time, there is a resonance explanation for 20 Hz responses. It
requires a squirting wave to travel, at the apex, from OHC1 to OHC3 in 50
ms, i.e., at a speed of several millimetres per second. Slow, but
physically realistic. Theoretical calculations of squirting wave velocity
based on the dimensions and physical properties of the organ of Corti
match that speed. So nature has solved the problem of how to tune the
cochlea over 3 decades of frequency, and it's based on dispersion and a
surface acoustic wave (SAW) resonator.

I come to the conclusion you haven't appreciated what the SAW model can
offer. I understand you haven't yet read my thesis, so I don't think it is
fair (to the readers on this list, at least) to try and conduct a rebuttal
of my points until you have.

Your post doesn't seem to advance the strength of the TW case. It just
resigns itself to having no explanation for how the stiffness and mass can
vary by a factor of a million, or, if not, how we can hear 20 Hz.

If you are looking for an answer, read about the squirting wave model in 
Bell and Fletcher 2004 (JASA, 116, 1016-1024). Have you not read that
reference, either?


Andrew Bell
Research School of Biology
Australian National University
Canberra, ACT 0200

On Thu, March 18, 2010 9:05 pm, reinifrosch@xxxxxxxxxx wrote:
> Hello !
> I, too, would be glad if the cochlear-mechanics discussion on the
> Auditory
> List could continue. If possible, the postings should be kept short.
> Today I would like to continue my point-by-point comments
> on the posting of March 7 by Andrew Bell:
>> In addition to Martin's 2 pieces of evidence against the traveling wave
>>  model, we can add: [...]
>> 2. The variation in stiffness is inadequate to tune the cochlea from 20
>> to 20000 Hz. Three decades of frequency calls for a million times
>> variation in stiffness (more than between foam rubber and tungsten), and
>> this is in contrast to measurements of 2 or 3 orders at most. See Naidu
>> & Mountain
>> 1998, Hear Res 124, 124. Bekesy found the value to be about a
>> hundred-fold (p. 476 of Exp in Hearing).
> The human BM resonance frequency, f_BMR = (1 / 2pi) * sqrt(S / M) at
> the base appears to be about 20 kHz. At the apex, however, that resonance
> frequency may well be considerably greater than 20 Hz.
> Both in post-mortem and healthy cochleae, the travelling wave does
> not reach the BM resonance place. At given frequency >1 kHz the passive
> (active) response peak is basal of the BM resonance place
> by about 1.0 (0.5) octave distance. In homo, that distance is ~5mm.
> Reinhart.
> 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 .