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Re: Laws of physics and old history...
Andrew Bell wrote:
... between proponents of traveling wave models and those who are
uncomfortable with its complexity.
Is "uncomfortable with its complexity" really the problem? It's not
that complicated, really. You have some fluid whose only relevant
property is mass, and a compliant membrane whose only property is
compliance, and a bit of geometry, leading to a simple boundary-value
partial differential equation, the solution of which is traveling
waves. Yes, you need a basic education in mathematical physics or
engineering to understand it, but not any complicated math.
You will of course see apparent traveling waves in any collection of
resonators or other filters with graded time constants. But there
are reasons why those are not good models of how the cochlea works.
You can make such a parallel filterbank work moderately well as a
functional model, but only if the filter order is at least 6 or 8
(like an N=3 or N=4 gammatone filterbank); basic (second-order)
resonators have been often tried and rejected as giving bad
predictions for masking and such. So now if you want to connect to
some underlying physics, you need 6 or 8 state variables at each
location, not just displacements and velocities as in the
traveling-wave systems. It just seems too unlikely that there are
that many undiscovered energy storage elements at each place in the
cochlea. Perhaps the "squirting wave" can do it if there are a bunch
of very compressible elements in there somewhere -- but I am
uncomfortable with pushing all that complexity into unknown
micromechanics, when we have a simpler paradigm that fits the data
Ranjit Randhawa wrote:
... auditory patterns published by Dr. Harvey Fletcher, which showed
that for pure tones the maximum peak of activity occurs at the CF
location and decreasing peaks of activity at harmonic locations.
I'd be interested in knowing what you're referring to. I've never
seen anything like that in Fletcher's papers.
... the range of stiffness of the BM only varies by a factor of 6 or so
I'm not sure what that report is, or exactly what the "stiffness"
means there, but the "volume compliance", the ratio of volume
displacement to pressure, is proportional to some (5th?) power of the
membrane width, and inversely as some power (3rd?) of membrane
thickness; the powers mean that the thickness and width don't have to
vary by a huge ratio to span several orders of magnitude of tuning.
I don't have the numbers handy, but I'm pretty sure that they're out
there, and consistent with the entire range of hearing (this paper by
Cole, 1977: http://www.springerlink.com/content/p32n73j266g632r7/
shows a factor of 1000 tuning range from a factor-of-6 width
variation). Physical models have even been built, and they show
traveling waves consistent with their membrane properties (e.g.