two discreet sets of identical frequ. fire rates (Peter )

Subject: two discreet sets of identical frequ. fire rates
From:    Peter  <pfreihof(at)OPTUSNET.COM.AU>
Date:    Mon, 5 Aug 2002 21:12:56 +1000

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 (at) 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 (at) a 120 deg phase shift. yours, Peter.

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Electrical Engineering Dept., Columbia University