Mathematical Modeling of the Hearing Process: Proceedings of the NSF-CBMS Regional Conference Held in Troy, NY, July 21–25, 1980M.H. Holmes, L.A. Rubenfeld The articles of these proceedings arise from a NSF-CBMS regional conference on the mathematical modeling of the hearing process, that was held at Rensselaer Polytechnic Institute in the summer of 1980. To put the a=ticles in perspective, it is best to briefly review the history of suc~ modeling. It has proceeded, more or less, in three stages. The first was initiated by Herman Helmholtz in the 1880's, whose theories dominated the subject for years. However, because of his lack of accurate experimental data and his heuristic arguments it became apparent that his models needed revision. Accordingly, based on the experimental observations of von Bekesy, the "long wave" theories were developed in the 1950's by investigators such as Zwislocki, Peterson, and Bogert. However, as the ex?eri~ents became more refined (such as Rhode's ~wssbauer Measurements) even these models came into question. This has brought on a flurry of 'activity in recent years into how to extend the models to account for these more recent eXT. lerimental observations. One approach is through a device co~monly refered to as a second filter (see Allen's article) and another is through a more elaborate hydroelastic model (see Chadwick's article). In conjunction with this latter approach, there has been some recent work on developing a low frequency model of the cochlea (see Holmes' article). |
Contents
1 | |
An Analysis | 55 |
Basilar Membrane Response Measured in Damaged | 70 |
A Mathematical Model of the Semicircular Canals | 85 |
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Common terms and phrases
Acoust amplitude angular velocity approximation asymptotic basilar membrane mirror basilar membrane vibrations boundary conditions boundary layer Chadwick CM loss cochlea cochlear model constant cross section cupula damage damping dB SPL deflection dimensional dominant equations dr dt duct endolymph Evans and Wilson experimental fibers fluid frequency response function geometry helicotrema high frequency Holmes impulse response incompressible input integral interferometric inverse problem inviscid Khanna and Leonard layer expansion linear longitudinal low frequency macromechanics Mathematical Models measurements membrane mirror method motion neural phase neural tuning nonlinearity obtained parameters partition radians/kHz resonance root round window running wave scala tympani scala vestibuli semicircular canals shown in Figure sinh sinusoidal solution Sondhi sound pressure level stapes stiffness T₂ technique theory tone transmission line transverse tube tuning curves tympanic membrane utricle variable viscous wavenumber zero ди дх