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Re: Basilar-membrane oscillations.


The wine glass and tuning fork change tuning when partially submerged in water because of an impedance change.
The vibration travels through the glass or metal causing side to side displacement.
When the wave hits the water, it gets harder to displace the sides and some energy is reflected back,
causing the effective shortening of the oscillating object.  It's like waves hitting the side of a plastic kiddie pool,
some energy moves the side of the pool, some causes a smaller wave to bounce back.

In the ear, the membrane not partially submerged, but completely submerged in fluid.  In this case, there would
be no impedance change at a submergence boundary.  The impedance for forces (internal or external) acting to displace the membrane would be the same throughout the length of the membrane, provided the other localized fluid boundaries (the walls of the cochlea) are constant.  The fluid will act as a coupling device (to the walls of the cochlea...). If the viscosity of the fluid was high (which it apparently isn't) it would also act as a damping element.  Neither of these would change the speed of sound through the membrane or the oscillating frequency or speed of the "traveling wave" (if there is one, which there
probably isn't, as such). 

My theory is that the membrane would not move at all without the forces acting on it through the cochlear fluid. The
fluid is pushing the membrane and displacing it slightly. What looks like a wave in the membrane is a reflection of forces
caused by eddy currents in the fluid.  It may be that these displacements affect the hair cells enhancing or reducing sensitivity
as the angle of the membrane to the eddy currents changes.  Given the amount of energy it would take to displace the membrane, as it is surrounded by fluid, it seems unlikely that the nervous system is pumping enough energy in (through
what phospherous channels?) to do it.

I notice that the stapes is attached at the base in two places and that the lengths of the "legs" are not the same.
This would seem to create a rocking motion rather than a direct push on the oval window, and cause
sideways (more or less parallel to the window) currents in the fluid in addition to any lengthwise displacement.
I would guess we have turbulent flow in the cochlear fluid being sensed, probably damped, and possibly enhanced
by the membrane and hair cells.

Still no one has answered my question on the stiffness of the cochlear walls?

(No phd, sorry.)

-----Original Message-----
From: reinifrosch@xxxxxxxxxx <reinifrosch@xxxxxxxxxx>
To: AUDITORY@xxxxxxxxxxxxxxx
Sent: Wed, Mar 31, 2010 9:57 am
Subject: [AUDITORY] Basilar-membrane oscillations.

Dear colleagues, 

Sorry, one more posting on the stiffness of the basilar membrane.

In my message of March 27, I
mentioned the guinea-pig BM oscillation frequency of 2.3 kHz measured by Mammano
and Ashmore (1993), "Reverse
transduction measured in the isolated cochlea by laser Michelson
interferometry", Nature 365, 838-841. How much higher

would the frequency be if the liquid above and below the partition were removed?

One of my wine glasses when empty
oscillates at ~523 Hz. If it is filled with water, the frequency drops to ~311
Hz, i.e., by a major sixth. If the glass
is completely under water, the frequency is ~208 Hz, lower than when empty by as
much as a major tenth.

A tuning fork,
however, sinks from 440 Hz to ~415 Hz when immersed, i.e., by a semitone only.

I believe that in these cases, and also
in the mentioned guinea pig experiment, evanescent liquid-pressure waves occur.
In those, the liquid particles move
back and forth (whereas in travelling surface waves they move on elliptical
trajectories). The drop in oscillation
frequency of resonators by immersing is severe if the streamlines of the
evanescent waves are long. In the mentioned
guinea-pig experiment, at the beginning of the rectangular electric-current
pulse, the BM was raised at the pipette
location (pipette diameter 5 micro-m), and probably was lowered at places more
basal and apical by 30 micro-m or so.
The typical streamline length (approximately half-circular, from raised-BM place
to lowered-BM place) may have been ~50
micro-m. The liquid on both sides of the partition thus may have increased the
effective BM surface mass density from
~0.1 kg / m^2 to ~0.2 kg / m^2, and so decreased the BM resonance frequency by a
factor of ~sqrt(0.5) = 0.7, i.e. by
(very roughly) about half an octave.

An extrapolation of the exponential guinea-pig BM-resonator map that I
presented in Fig. 3 of "Old and New Cochlear Maps", Canadian Acoustics Vol. 37,
No. 3 (2009) 174-175, up to x = 11 mm
from base, yields a frequency of 3.7 kHz, greater than the mentioned
experimental result of 2.3 kHz by about a minor


Reinhart Frosch,
Dr. phil. nat.,
r. PSI and ETH Zurich,
Sommerhaldenstr. 5B,
CH-5200 Brugg.

0041 56 441 77 72.
Mobile: 0041 79 754 30 32.
E-mail: reinifrosch@xxxxxxxxxx .