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Re: Laws of physics and old history...

Dear Randy and list:

I've been listening in on this conversation, and it does seem to have become
a tennis match between proponents of traveling wave models and those who are
uncomfortable with its complexity. Personally, I'm in the second camp, but
it's not a matter of casting votes. What we need are clear, considered
arguments, starting from first principles. 

Randy mentions resonance models, and here my interest is aroused. I have put
forward a resonance model in which the resonant elements are tiny parcels of
fluid in the subtectorial space which are shuttled back and forth by the
rows of outer hair cells. This surface acoustic wave (SAW) model involves
the conversion of pressure waves with extremely long wavelengths to
"squirting waves" with very short wavelengths (about 30 um, which is the
distance from OHC1 to OHC3). Because squirting waves are highly dispersive
(wavelength proportional to 1/(f^3)), the distance between the OHC rows can
tune the cochlea from 20 Hz at the apex to 20 kHz at the base, just as Randy
was wanting. References are below. 

And speaking of laws of physics and old history, I have gone back to the
history of the middle ear muscles and reviewed their workings. In the 1880s,
Gellé developed an "intralabyrinthine pressure theory" of how these muscles
protect the cochlea. Intuitively appealing, the ILP theory says that when
the middle ear muscles are activated, they push the stapes inwards and raise
the pressure in the cochlear fluids, protecting it from overload. The theory
was put aside because people couldn't see how pressure could affect
traveling wave mechanics. Now, with the possibility that OHCs are pressure
sensors, I propose a revival of the old ILP theory in a recent review paper.
For those interested, it is available open access at
It's also a case study of what happens when a particular model dominates a
field and prevents open-minded consideration of alternatives. 



Bell & Fletcher (2004). The cochlear amplifier as a standing wave:
"squirting" waves between rows of outer hair cells? JASA 116:1016-24.

Bell (2010). The cochlea as a graded bank of independent, simultaneously
excited resonators: calculated properties of an apparent 'travelling wave'.
Proceedings, International Congress on Acoustics, Sydney. 

Bell (2005). The Underwater Piano: A Resonance Theory of Cochlear Mechanics.
PhD thesis, The Australian National University, Canberra. 

Dr Andrew Bell
Research School of Biology (RSB)
College of Medicine, Biology and Environment
The Australian National University
Canberra, ACT 0200, Australia

> -----Original Message-----
> From: AUDITORY - Research in Auditory Perception 
> [mailto:AUDITORY@xxxxxxxxxxxxxxx] On Behalf Of Ranjit Randhawa
> Sent: Thursday, 10 November 2011 6:18 AM
> To: AUDITORY@xxxxxxxxxxxxxxx
> Subject: Re: [AUDITORY] Laws of physics and old history (A 
> new paradigm?(On pitch and periodicity (was "correction to post")))
> Dear List,
> As the mathematics of the proposed models get hairier one has to look 
> back in history to some results of 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. The extant of such a pattern increases 
> with stimulus 
> strength, that is towards the basal end. I am not sure whether these 
> results have been universally accepted, I for one have not seen any 
> criticisms, but I find support in that, ISI's have been reported to 
> reliably exist at integer fractions of the fundamental period of the 
> stimulus, thereby indicating some sustained activity at the 
> harmonics. 
> It has also been reported, again I have no reason to dispute 
> this, that 
> the range of stiffness of the BM only varies by a factor of 6 or so, 
> while our frequency range would demand a much larger number. If any 
> model appeals to resonance as the basis of BM movement, then such 
> resonance elements would have to be shown to have the 
> required range of 
> our hearing. With these observations, proposals using linear or 
> non-linear models using only passive elements, then compressing a 
> stimulus wavelength measured in meters to a length which is a 
> fraction 
> of 32 mm are hard to accept, irrespective of what the associated 
> mathematics used by the models may show. I have my own doubts of how 
> these equations are being interpreted, but I shall leave it 
> to the rest 
> of the auditory community to come to their own conclusions.
> Thanks, cheers,
> Randy Randhawa
> On 10/31/2011 10:39 PM, Steve beet wrote:
> > I'd just like to add my vote to Dick Lyon's interpretation 
> of the laws 
> > of
> > physics: in the cochlea the "free-space" speed of propagation in the
> > perilymph / endolymph would be very high but the transverse 
> dimensions of
> > the structures within the cochlea are small. Consequently 
> there should be
> > only one mode of propagation in the normal audio frequency 
> range - although
> > I'm not sure how well the concept of "modes of propagation" 
> fits with
> > non-uniform partially-elastic structures such as those 
> found in the cochlea.
> >
> > > From the evidence I've seen, the speed of propagation within the 
> > > cochlea is
> > almost entirely determined by the elasticity and dimensions of the 
> > basilar membrane, and the density and viscosity of the 
> fluids in the 
> > cochlea. The other structures within the cochlea (notably the 
> > tectorial membrane and the active effects of the OHCs) also 
> need to be 
> > accounted for if you want a truly accurate model, but I can see no 
> > reason to suppose that they are even linear, let alone 
> quantifiable in 
> > terms of a simple transmission-line model.
> >
> > Steve Beet
> >
> >
> >
> > -----Original Message-----
> > From: AUDITORY - Research in Auditory Perception 
> > [mailto:AUDITORY@xxxxxxxxxxxxxxx] On Behalf Of Richard F. Lyon
> > Sent: 31 October 2011 21:47
> > To: AUDITORY@xxxxxxxxxxxxxxx
> > Subject: Re: A new paradigm?(On pitch and periodicity (was 
> "correction 
> > to
> > post"))
> >
> > In the ear, the stapes doesn't couple much energy into this fast 
> > pressure-wave mode.  A much slower propagating vibration mode is 
> > involved in the cochlear traveling waves that use the compliance of 
> > the basilar membrane, as opposed to compression of the 
> fluid, as the 
> > displacement-based restoring force that leads to the wave equations.
> >