On the Dynamics of the Cochlea
Harvey Fletcher · The Journal of the Acoustical Society of America · 1951
This paper is concerned with the dynamical behavior of the cochlea. 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. The boundary conditions at the stapes end is simply that the pressure difference in the two canals is equal to P0 any desired pressure difference. However, at the helicotrema the pressure difference must be equal to that between the two ends of the capillary opening at the helicotrema. Then from the fundamental hydrodynamical equations and the experimental constants obtained by Békésy it is shown that the speed of sound through the liquid of the inner ear may be considered infinite compared to the speed of the wave along the basilar membrane. In other words, 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 the fundamental dynamical equations and found to be in good agreement with the experimental results of Békésy; (a) displacement amplitudes and phases of the basilar membrane at different distances from the stapes and for different frequencies, (b) time for wave to travel from stapes to various distances from stapes, and (c) volume displacement, at various frequencies, per dyne difference of pressure at oval window and that at round window.