[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

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

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.