Basic Linear Tools

Abstract

This chapter presents some elementary tools which are used to analyze physical properties of (some of the constituents of) the cochlea. Acoustic signals depend strongly on the properties of the sound carrying medium. Vacuum, or an incompressible nonabsorbing wall, blocks propagation. Up to the middle ear the medium is air, with propagation properties that depend on temperature and humidity. The cochlea (and the connected vestibular system) are fluid filled with perilymph or endolymph, the acoustic properties of which approach those of water. In water, we can distinguish bulk waves and surface waves (in which the compressibility of the medium is essential), from fluid displacement waves (which depend on the mobility of the fluid but do not require compressibility). In the latter case, the mobility is primarily constrained by properties at the boundaries and fluid inertia. The displacement waves will turn out to dominate acoustic fluid motion in the cochlea. This can be deduced from the comparison of properties of sound waves in water and the dimensions of the cochlear ducts. It turns out that the velocity of sound in the fluid is so high, ≈ 1. 5 km/s—and consequently its wavelength is so large with respect to the cochlear dimensions—that for most mammals the cochlear fluid can be considered as incompressible. This implies that the velocity of sound within the cochlear fluid is practically infinite. For frequencies above about 10 kHz, this approximation needs to be refined. Then propagation begins to become noticeable. For larger cochleas than the human case, the frequency boundary will be shifted downward, for tinier cochleas it will be higher. Note that some bat species have a high-frequency limit of their echo location frequencies range that extends beyond 100 kHz, and in such cases the phase effects due to compressibility have to be taken into account.