Subject: Cochlear liquid-particle trajectories. From: "reinifrosch@xxxxxxxx" <reinifrosch@xxxxxxxx> Date: Thu, 31 Aug 2006 10:37:03 +0000Dear List, The calculations on the "new" basilar-membrane stiffness formula take longer than expected. If they give interesting results, I shall communicate them in a week or two. Yesterday I received a cochlear-mechanics report on a transmission-line model, containing a graph of liquid streamlines which disagree with what I have learned. In the case of small-displacement surface waves on the ocean it is helpful to change to a coordinate system which moves along with the wave crests: x' = x - c * t (where x = longitudinal coordinate, t = time, c = phase velocity). In the primed coordinate system, the liquid particles make a stationary flow in the -x'-direction. At the crests, the streamlines are far apart from each other, so that the velocity v_x' of the particles is comparatively low. Transformation back to the lab system yields closed, elliptical liquid-particle trajectories (circular for short waves). In long waves (e.g., tsunamis far from the coast) the particle trajectories are oblong ellipses; at the ocean floor, the length of the short ellipse axis is zero. In cochlear waves, the phase velocity c decreases if x increases; the liquid-particle trajectories, however, are similar (I believe) to those in ocean waves, i.e., closed and approximately elliptical. The elliptical particle trajectories do not cross the basilar membrane (BM). At the BM, the liquid particles move along the BM. That is why the mass of the organ-of-Corti cells (which in the idealistic models do not move along the BM) plays a role even if their density is equal to that of the liquid. A good introduction into cochlear waves was written by the late G.K. Yates: Chapter 2 of the book "Hearing", B.C.J. Moore, ed., Academic Press, San Diego, 1995, Section II.B, pages 49-53. With best wishes, Reinhart Frosch. Reinhart Frosch, Dr. phil. nat., r. PSI and ETH Zurich, Sommerhaldenstr. 5B, CH-5200 Brugg. Phone: 0041 56 441 77 72. Mobile: 0041 79 754 30 32. E-mail: reinifrosch@xxxxxxxx .