Contribution of Even/Odd Sound Wave Modes in Human Cochlear Model on Excitation of Traveling Waves and Determination of Cochlear Input Impedance

Wenjia Hong,Yasushi Horii

doi:10.3390/acoustics4010011

Abstract

Based on the Navier–Stokes equation for compressible media, this work studies the acoustic properties of a human cochlear model, in which the scala vestibuli and scala tympani are filled with compressible perilymph. Since the sound waves propagate as a compression wave in perilymph, this model can precisely handle the wave–based phenomena. Time domain analysis showed that a sound wave (fast wave) first propagates in the scala vestibuli and scala tympani, and then, a traveling wave (slow wave) is generated by the sound wave with some delay. Detailed studies based on even and odd mode analysis indicate that an odd mode sound wave, that is, the difference in the sound pressures between the scala vestibuli and scala tympani, excites the Békésy’s traveling wave, while an even mode sound determines the input impedance of the cochlea.

Highlights

Model on Excitation of TravelingAccording to Békésy’s traveling wave theory [1], the basilar membrane (BM) in the cochlea plays an important role in analyzing the frequency spectrum of sound waves.The BM has a long trapezoid shape, and becomes narrower and thicker near the base of the cochlea
At 10,000 Hz, the wavelength was only λ = 152 mm, and the 35 mm cochlea corresponded to about a quarter wavelength of the sound wave
Since the total length of the scala vestibuli (SV) and scala tympani (ST) was about 70 mm, the oval window (OW) and round window (RW) were located at a half wavelength distance at this frequency

Summary

Introduction

According to Békésy’s traveling wave theory [1], the basilar membrane (BM) in the cochlea plays an important role in analyzing the frequency spectrum of sound waves. This paper designs a cochlear model assuming that the perilymph in the SV and ST is compressible, and explains the excitation mechanism of a traveling wave based on even and odd mode analysis [14]. This is a basic technique that has been used for a long time in microwave engineering for designing parallel couplers and explaining the principle of undesired crosstalk on analog phones. We would like to emphasize that it is indispensable to define the perilymph as a compressible medium to discuss the even and odd mode approach

Modeling

Frequency Domain Analysis

Time Domain Analysis

Conclusions