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Cochlear travelling waves.

Dear colleagues,

Since the List is very quiet now, I permit myself to post a second comment on the paper "MoH 101: Basic concepts in the mechanics of hearing", by Bergevin, Epp, and Meenderink, in the recently published proceedings volume "What Fire Is in Mine Ears: Progress in Auditory Biomechanics". In their section "What are the requirements for traveling waves in the ear", the authors have written: "As the membrane moves, it changes the volume on both sides of its given radial location. If the fluid is incompressible [...], the fluid must move longitudinally along the tube (conservation of mass)."

My comment: The motion of the liquid in the cochlear scalae during the perception of a tone differs strongly from the motion of a liquid streaming through a tube as usually treated in hydrodynamics courses. Near the best place [place of maximal excitation at low sound-pressure level], the liquid motion is restricted to two narrow regions just above and below the cochlear partition [basilar membrane (BM) and attached organ-of-Corti cells]. If the BM is in the xy-plane and the x-axis points towards the cochlear apex, then the liquid particles just above and below the BM near the best place move on closed circular trajectories in planes approximately parallel to the xz-plane. Measurements of Recio et al. (1998) in chinchilla at x = 3.5 mm from base, at a level of 104 dB (SPL), imply that at the tone frequency yielding the maximal excitation (7 kHz), the radius of the mentioned circular liquid-particle trajectories amounts to about 1.4 micrometer only. [For comparison: The distance between the centers of two adjacent inner hair cells is about 10 micrometers]. 

As mentioned yesterday, this liquid motion is similar to that in gravity surface waves on lakes, where circular liquid-particle trajectories in vertical planes are observed if the wavelength is short compared to [(2pi) times (water depth)]. At the lake surface, the trajectory diameter is equal to the wave height. Below the surface, that diameter decreases. At one wavelength below the lake surface, the trajectory diameter is shorter than that at the surface by a factor of exp(-2pi) = 0.0019.    
Reinhart Frosch,
CH-5200 Brugg.
reinifrosch@xxxxxxxxxx .