-----Original Message-----
From: AUDITORY - Research in Auditory Perception [mailto:
AUDITORY@xxxxxxxxxxxxxxx] On Behalf Of Matt Flax
Sent: Monday, March 08, 2010 2:16 PM
To:
AUDITORY@xxxxxxxxxxxxxxx
Subject: Re: [AUDITORY] mechanical cochlear model
The concept that the passive inner ear mechanism does not conduct energy
as a fast pressure wave (with long wavelength) may be true - however not
everyone agrees on this point. I believe that you are talking about the
coupling between the outer ear and the inner ear below - and thus the
passive action of the hearing system.
The concept that the active inner ear mechanism is an active travelling
wave seems a little impossible (from what people have discussed
previously - experimental evidence and theory) for any location other
then the base of the inner ear. I stand on record as the first for
claiming that the base is dominated by the active travelling wave and
the mid/apex is dominated by the active long pressure wave (my
compression wave cochlear-amplifier definition).
Matt
On Mon, 2010-03-08 at 07:52 -0800, Richard F. Lyon wrote:
> Alain, your "simple account" was "reasonably correct" whether you
> mentioned the traveling wave or not, so I agreed with you.
>
> I admit I don't see why you don't explicitly identify that account
> with traveling waves. Sinusoids in such a system are locally
> described as cos(ometa*t - k*x), with some varying amplitude, where
> the relations between omega and k locally obey the same kind of
> dispersion relation (more or less) as gravity waves on water.
>
> The real issue seems to be about where the energy is, and how it
> propagates and gets detected. The fast pressure wave is another
> physical mode that really exists, but its wavelengths are all very
> large compared to the cochlea, so the pressure due to this mode can
> be viewed as equal throughout the cochlea; pushing on the stapes
> immediately pushes out at the round window. But this mode doesn't
> carry much energy, as the middle ear leverage isn't nearly enough to
> couple efficiently to it; there's also no efficient way to get energy
> back out of this mode into a place and a form for which detectors are
> known; the fast compression wave therefore carries pressure, but not
> much energy. The traveling wave mode, on the other hand, involves
> much larger fluid displacements at the same pressures; it's a
> differential mode between the scalae, propagated by the spring of the
> BM instead of by fluid compression. And the energy converges on the
> BM as the wave slows down and the wavelength gets short, focusing the
> energy into a small layer with large displacements at the BM. There,
> the hair cells, which evolved to detect fluid motion via cilia
> bending, are well positioned to respond.
>
> A wave has three kinds of delays: phase, group, and wave-front. In
> typical models, the wave-front delay is essentially zero, and the
> response latency can be made to approach zero as the level gets very
> high. The group delay depends on the damping, including negative
> damping effects, and so varies a lot with level. The phase delay is
> in between, around a cycle and half, and pretty stable. Pretty much
> everything about it is as Lighthill described, in terms of energy
> flow, except that there's not much BM mass so it's not really
> significantly resonant, except for very high frequencies very near
> the base where the accelerations are very high. And except for some
> positive feedback from outer hair cells that modifies the dispersion
> relation, providing active gain instead of loss over some range of
> wavelengths.
>
> If it walks like a wave, and quacks like a wave, and transports
> energy like a wave, why not call it a wave?
>
> Dick