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Re: AUDITORY Digest - 8 Mar 2010 (#2010-55)

On 09 Mar 2010, at 12:06 AM, AUDITORY automatic digest system wrote:

> On Tue, Mar 9, 2010 at 11:25 AM, Lloyd Watts <lwatts@xxxxxxxxxxxx> wrote:
>> Rhode's 1971 data showed about 3-4 cycles of phase accumulation to the best
>> place, independent of amplitude.  I believe that is strong evidence of a
>> traveling wave that takes 3-4 cycles to arrive, and I believe from
>> discussions directly with Bill in 2000-2003 that this is also how he
>> interpreted his measurements.
>> Regarding the stiffness change not being sufficient to explain 3 orders of
>> magnitude of frequency, I believe that argument is based on the assumption
>> of constant membrane mass (what I called in my thesis, the constant-mass
>> scaling assumption, which does indeed imply 6 orders of magnitude of change
>> of stiffness from base to apex, and the damping decreases by 3 orders of
>> magnitude).  But the widening of the basilar membrane is more consistent
>> with an increasing-mass assumption, in which the stiffness decreases, the
>> mass increases, and the damping remains constant.  Neither is probably
>> exactly correct, but it shows that having all the change in the stiffness is
>> not necessary, and the widening of the basilar membrane is consistent with
>> both a mass increase and a stiffness decrease.

Hi, Lloyd, all. Long time, etc.

What I've always found challenging and confounding about the cochlear traveling wave -- and I'm pretty sure that I'm not alone -- is that while the cochlear partition velocity or amplitude distribution has the *form* of a traveling wave -- albeit, one with spatially varying magnitude and phase, both explained in modeling by using the LG/WKB/phase-integral solution to the sinusoidal steady-state dynamical equations -- that wave has the unusual characteristic that the Poynting vector is perpendicular to the direction of motion: The wave propagates from base to apex, but the energy flows into (passive cochlear-partition model) the cochlear partition along its length. 

The kinds of intuitions we've developed about traveling waves in air or along stretched strings just don't hold. It's a different beast, since the fluid motion in the scalae has to obey Laplace's equation, the boundary conditions of the scalae and partition geometry (cross-sectional area shape, moving width, etc.), and the pressure across and velocity of the partition are constrained by the assumed partition impedance. As Lloyd notes, it's not just the variation of the stiffness that yields the cochlear map, but the variation of the stiffness and mass and, I would argue, damping, too. There are only certain combinations of assumed exponential rate constant for each of stiffness, mass, and damping that yield magnitude and phase distributions that resemble observations. [Wilson, T. A. (1998). “Rejecting a constant-mass model for cochlear-partition dynamics.” Proceedings of the Joint Meeting of the Acoustical Society of America and the International Conference on Acoustics.] [Wilson, T. A. (1996). “Mechanical cochlear-partition parameter variation in a box-cochlea model.” J. Acoust. Soc. Am., Vol. 100, No. 4, Pt. 2.] 

Timothy Wilson, Sc.D., P.E.
Chair and Professor
Department of Electrical, Computer, Software, and Systems Engineering
Embry-Riddle Aeronautical University - Daytona Beach Campus
wilsonti@xxxxxxxx | http://faculty.erau.edu/wilsonti/