On the Dynamics of the Cochlea

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Abstract
It is assumed that a length of the basilar membrane which is equal to its width at each position vibrates as a unit, and that the forces exerted upon it by adjacent units are negligible compared to that exerted by the difference in pressure in the scala vestibuli and scala tympani. At the stapes end any desired pressure difference in the 2 canals may be produced. At the helicotrema the pressure difference must be equal to that between the 2 ends of the capillary opening at the helicotrema. From fundamental hydrodynamical equations and exptl. constants obtained by Bekesy it is shown that the speed of sound through the liquid of the inner ear may be considered infinite compared with the speed of the wave along the basilar membrane. The liquid may be considered incompressible so that the rate of liquid displacement at the oval window is equal to that at the round window, and is also equal to that produced by flexure of the basilar for frequencies above 200 cps. Below this frequency some of the liquid goes back and forth through the helicotrema. With these assumptions, the following quantities were calculated from fundamental dynamical equations and found to be in good agreement with exptl. results; displacement amplitudes and phases of the basilar membrane at different distances from the stapes and for different frequencies; time for wave to travel from stapes to various distances from stapes; and volume displacement, at various frequencies, per dyne difference of pressure at oval window and that at round window.

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