A hydrodynamical theory is given for a model of the cochlea. The model consists of two channels of varying but equal cross sections. The channels are separated by an elastic membrane with variable dynamical constants. The two channels are interconnected at one end, and the entire structure is rigidly enclosed except for two accessible areas corresponding to the round and oval windows. The equations of motion, continuity including the effect of the membrane, and appropriate boundary conditions are formulated. As a first step towards a complete analysis the non-dissipative case is considered. Numerical solutions are found using experimental data obtained by G. v. Békésy. Localization phenomena and phase velocities are found to be in broad agreement with experimental data.
Results are given of measurements made on a 175-section network representing the basilar membrane, which was modified to include the effects of dissipation in the cochlear partition. The results show that the dynamical theory of the cochlea, when dissipation is considered, is in good agreement with experimental evidence.T is the purpose of this paper to describe some results, determined experimentally, pertinent to a dynamical theory of the cochlea. This theory, developed in a recent paper, x gives equations which govern the dynamics of a theoretical model of the cochlea. The equations include the effects of dissipation in the cochlear partition and viscous losses in the fluids filling the scalas vestibula and tympani. Solutions were given only for the case in which dissipation in the cochlear partition was disregarded. The equations referred to give the pressures in the fluids on either side of the cochlear partition and the displacement of the basilar membrane, both as a function of frequency and the distance along the membrane from the stapes to the helicotrema.In the course of the work described in reference 1, an electrical network was builff' which would act as an analog to three of the equations* whose solutions were ß desired. The network, as originally designed and built, was to give solutions to the equations for the case in which dissipation was neglected. Such unwanted dissipation as actually existed in the network was due to unavoidable loss in the constituent elements. The quantities found by the network are the pressure differx L. C. Peterson and 13. P. 13ogert, J. Acoust. Soc. Am. 22, 369 (1950). ' B. P. Bogerr, Bell Labs. Record 28, 11, 481-485 (1950). * Equations (14), (15), and (16) of reference 1. ence across the cochlear partition (P_) and the displacement of the basilar membrane (Y), as functions of distance x from the stapes and angular frequency co. The network, shown in Fig. 1, was subsequently modified to include the effect of dissipation or damping in the cochlear partition. In this manner, the effect of r(x), representing the damping, could be determined with reasonable accuracy and with much less labor than by numerical calculations. The effect of viscosity of the fluids filling the scalas is ignored. The network has 175 sections, each section with the configuration shown in Fig. 2. The series inductance Lx represents the mass of the fluid in the scalas vestibula and tympani, and the dotted condenser Cx represents the compressibility of the fluids.• The shunt impedance represented by the coil L•., resistance R1, and set of three condensers C2, Ca, and C4 corresponds to the assumed dynamical properties of the cochlear partition. The voltage across the line corresponds to the pressure difference P_(x, co), and the voltage at the junction of the condensers Ca and C4 corresponds to the membrane displacement Y(x, co).The addition of resistance R1 to the shunt impedance enabled the determination of the results to be described here.
In the winter of 1959‐1960, a Columbia long‐period vertical seismometer was set up at the Chester Field Laboratory, Bell Telephone Laboratories, Chester, New Jersey, 69 kilometers west southwest of Palisades. The vault is located at 40°‐47.6′N, 74°‐40.3′W. The instrument was installed to obtain recordings of surface waves for digitization and analysis on an electronic computer. The seismometer had a free period of 30 seconds, and by use of a capacitor across the output terminals, the effective period was increased to 60 seconds.
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