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Re: A new paradigm?(On pitch and periodicity (was "correction to post"))
On Thu, 6 Oct 2011 10:44:07 -0700
"Richard F. Lyon" <DickLyon@xxxxxxx> wrote:
> My impression is that "transmission line models" is too tied to
> one-dimensional or long-wave approximations. Am I wrong? Is it the
> case that you can make a 1D electrical transmission-line analog of a
> 2D or 3D hydrodynamic traveling-wave system? Or do you mean to
> include 2D electrical analogs in what you call transmission-line
> models? We just need to be clear what the scope of your preferred
> term is.
I agree that transmission-line models are tied to long-wave approximations in most people's minds, and that that is a significant weakness, but the models can often be modified to better approximate 'real' 3-D wave propagation, without discarding them completely.
In my PhD thesis (on processing of deep-sea divers' speech) I spent quite some effort modelling the effects of vocal tract wall vibration on speech production. The vocal tract is significantly different from the auditory system (the wave propagates in a compressible medium, with an elastic and damped boundary, the source impedance varies with time, etc., etc.) but in the case of the vocal tract, it was possible to approximate 3-dimensional effects by making the speed of sound propagation frequency-dependent, and taking account of different 'modes of propagation'.
Analysing the dimensions, the elasticity and density of the vocal tract wall allowed me to come up with a pretty realistic model of the variation of sound velocity (and hence acoustic impedance) with frequency. The different 'modes of propagation' of sound waves in both elastic and non-elastic tubes has been extensively investigated over the years.
I haven't tried to model the auditory system in the same way, but I suspect it would be worth a try. There are two factors which seem somewhat specific to the auditory system:
1) the elasticity and mass of the basilar membrane and associated structures vary along its length
2) the speed of propagation of the sound wave in the cochlea is not simply due to the elasticity of the basilar membrane - it also needs to be modified to take account of the propagation of the wave from the basilar membrane back to the round window, the elastic properties of the round window itself, and possibly Reissner's membrane
I'd welcome any comments on this, although I doubt I will find time to pursue it myself.