Re: Laws of physics and old history... ("Richard F. Lyon" )

Subject: Re: Laws of physics and old history...
From:    "Richard F. Lyon"  <DickLyon@xxxxxxxx>
Date:    Wed, 9 Nov 2011 19:14:13 -0800

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 pretty well. 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: 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. ). Dick

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