two discreet sets of identical frequ. fire rates

[Peter <pfreihof@xxxxxxxxxxxxxxx>]

Hi Martin,

you wrote:
.......................
The two 24 Hz waves, one air conducted and another one bone conducted
and phase
shifted, will superimpose on the basilar membrane to ONE sinusoidal
wave with a frequency of 24 Hz and a phase and amplitude depending on
the amplitude ratio and phase difference between of the two primary
waves.
......................
I would say, this is typically the case for any linear system.
But wouldn't the bone conducted 24 Hz component be somewhat subject to
nonlinearities in that the resulting pressure wave exciting the cochlea
"from the outside" could produce distortions similar to intermodulation?
I mean, the positive and negative excursions of this bone conducted wave
could lead to asymmetric movements of the basilar membrane relative to
the tectorial membrane - no?
Just imagine, the vibrational wave already had just crossed the zero
line (thus generated a pulse) in a group of hair cells, and while this
particular group relaxes, another (this time acoustic) wave zero
crossing arrives, in a somewhat untimely fashion (120 deg, instead of
180), finding this particular hair cell group unprepared to fire again.
In an analog system (like a single transmission medium f.e. air), the
already deflected air molecule just gets deflected a little more, thus
accommodating the sum of the two pressure waves. But neurons which only
can react by firing at a zero crossing cannot accommodate this special
case of two zero crossings in close succession.
I assume hair cells can only move in sinusoidal fashion, hence exhibit a
180 deg firing pattern - unless it is not subject to any excitation in
which case it would fire randomly.
................
Your proposed idea would otherwise suggest that you should be able to
generate pulse trains corresponding to any multiple of 24 Hz,
e.g. 4*24 Hz if air conducted and bone conducted sound had a phase
shift og 360/4 degrees, etc.  Higher multiples would just require more
and more "random fire pulses hitting the missing spots".
...................
This thought also occurred to me.
But, as pointed out earlier, there are only two 120 deg phase shifted
components in the beginning (acoustic and vibration), and the third
component is generated by the random firing (and possible generation of
a phase tailored selective amplification OAE at 72 Hz?).
If you took your example 360/4 - this would create 4 pulse trains of 90
deg phase shift (which of course, would require more than the the two
existing separated transmission media air/ear drum and earth/bone). Even
if there would be three transmission channels, the 360/4 example would
result in two pairs of 180 deg phase shifted pulse trains which of
course cancel themselves out.
The availability of two separate transmission channels in which phase
shifts of 120 deg @ the same frequency can be accommodated, creates a
succession of positive and negative going zero crossings.
This would look exactly the same as a true 72 Hz pulse train, arriving
through only one transmission channel like air, or bone.
The question truly is, can the bone conducted component create a
mechanical vibration of the cochlea, which is different in phase to the
additionally applied acoustic component.
There is also the possibility of nonlinear distortions due to the
"unnatural" addition of two phase shifted sine waves at their meeting
point on the basilar/tektorial membranes.
Just note, in case of natural bone conduction for low frequencies, these
would always be in phase with the acoustic component due to the short
distance from the receiving body part to the inner ear, if there is only
(atmospheric) sound pressure involved.
But this scenario is about vibrations from the ground, entering the
body, while acoustic components enter the ear @ a 120 deg phase shift.

yours,
Peter.