Inselberg A. & Foerster H. von (1970) A mathematical model of the basilar membrane. Mathematical Biosciences 7: 341–363.
A mathematical model of the basilar membrane.
Mathematical Biosciences 7: 341–363.
A two-parameter basilar membrane model with uniform geometry, mass, and stiffness distribution is studied. The exact solution of the equation of motion is obtained. For certain model configurations the displacement patterns of the membrane consist of traveling waves and damped standing waves. A place principle is observed with the direction of the shift governed by the relative magnitudes of the model parameters. The qualitative effect of a stiffness gradient along the membrane on the place principle is discussed. Thresholds, with respect to frequency, are found that suggestthat the location of the low-frequency threshold depends only on the membrane length.
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