Re: A new paradigm?(On pitch and periodicity (was "correction to post"))

["Richard F. Lyon" <DickLyon@xxxxxxx>]

Willem, your approach in which "the flow behaves as a parallel 
streaming oriented along the core of the perilymph duct" and in which 
"there exists only a contribution in the x-direction" is what might 
be called a "non-compliant membrane" approximation.  Generally, the 
BM is interpreted as being variably compliant (and the RM very 
compliant), such that there is some velocity (and pressure variation) 
ortogonal to the x dimension, which corresponds to BM displacement. 
If you assume no BM displacement, then of course you have no 
traveling wave.

The BM (or the whole of scala media in your approximation) separates 
the two parts of the folded duct in which you have a longitudinal 
pressure gradient, so there will be a substantial pressure difference 
across it, from the far-apart x locations (except near the apex where 
it folds).

If you allow the pressure across the BM to deflect it, as we usually 
do with membrane compliance, you get a very different analysis, based 
on the same physics but different mechanical approximations.  In this 
analysis, the v-squared pressure differences due to Bernoulli's law 
are generally very small compared to the pressure differences 
accelerating the fluid within the short wavelength of the traveling 
wave, so are neglected.

Which approximation is better?  Probably the one that yields a 
traveling wave like the one seen in direct mechanical measurements, I 
think.

Dick