Frequency selectivity without resonance in a fluid waveguide

Abstract

This study analyzes a waveguide consisting of two parallel fluidfilled chambers connected by a narrow slit that is spanned by two coupled elastic beams. A stiffness gradient exists in the longitudinal direction. This simple linear system, which contains no lumped mass, is shown to act as a spectral analyzer. Fluid waves traveling in the waveguide exhibit a distinct amplitude peak at a longitudinal location that varies systematically with frequency. The peaking is not based on resonance, but entirely on wave dispersion. When entering its peak region, the wave undergoes a sharp deceleration associated with a transition in which two propagation modes exchange roles. It is proposed that this mode shape swapping underlies the frequency analysis of the mammalian cochlea.avoided crossing | tonotopy | group velocity | hydrodynamics | auditory filter I n this study I explore the following question: How can a waveguide act as a spectral analyzer which spatially separates the frequency components of a wideband input? This question has been debated since Bekesy's observation of traveling waves in the mammalian inner ear (1), the cochlea. On their way from base to apex, these fluid waves exhibit an amplitude peak at a frequency-dependent place. The peaking underlies our ability to identify and separate sounds.The most common explanation of cochlear frequency selectivity invokes local resonances coupled to the traveling wave (2). This approach requires a form of mass loading of the cochlear partition in addition to the mass loading by the surrounding fluid. The amount of mass needed in such models has been criticized for being unrealistically large given the cochlear anatomy (3). Even when sidestepping these objections, it has proved difficult to formulate models that reproduce both the amplitude and phase data of sensitive cochleae. On their way to the amplitude peak, cochlear traveling waves accumulate only 1-2 cycles (4, 5). Resonance-based models that produce sharp amplitude peaking tend to systematically overestimate the phase accumulation (6, 7). The resonance point acts as a cutoff, and a hypothetical frictionless wave would accumulate an infinite number of cycles when approaching it (8). Although damping will temper this singular behavior, too much of it also spoils the amplitude peaking.In active cochlear models (9, 10) this problem is circumvented by postulating a limited region of mechanical amplification ("negative damping") basal to the resonance point. This creates a sufficiently sharp amplitude peak at a more basal location (safely away from the singularity), while still allowing ordinary damping to temper the phase accumulation near the resonance point (7).The present study explores an alternative approach which rejects resonance as the mechanism producing the peaking. In this scenario the peaking of traveling waves is created by a form of wave dispersion that is characterized by a steep deceleration of the energy transport. The deceleration produces a densification (focusing) of the energy that creates the pe...

Noninvasive in vivo imaging reveals differences between tectorial membrane and basilar membrane traveling waves in the mouse cochlea

“…Modeling efforts have demonstrated how differential motion between two parallel structures could lead to sharp frequency tuning (44)(45)(46). The differences between the TM and the BM traveling waves that we measured strongly support this concept.…”

Reticular lamina and basilar membrane vibrations in living mouse cochleae

“…Phase inconsistency between our results and others' likely resulted from differences in phase detection techniques, animal species, and measurement locations. Whereas the proposed cochlear micromechanical mechanism is well supported by experimental data, it does not exclude other mechanisms (33,(39)(40)(41)(42)(43)(44)(45)(46)(47)(48)(49).…”

Power Dissipation in the Cochlea Can Enhance Frequency Selectivity

“…It is possible that the organ of Corti tissue or the tectorial membrane is so soft that they behave more like a fluid than a solid or that the OCC mass is negligible. Indeed, there are studies that neglected the effect of OCC inertia ( 26 , 64 ). Had we overestimated the OCC mass so that structural mass became more dominant than extra-OCC fluid inertia, the intra-OCC damping property could be overestimated as well.…”