Dear colleagues,
The abstract included below was recently accepted for a poster presentation by the organizers of an international conference to be held next summer. Now I decided to not attend that conference and therefore to withdraw the contribution. I plan to submit a similar abstract for a later conference. The main ideas of the described analysis are presented in Chapters 26 and 44 of my new book, "Introduction to Cochlear Waves", available via the publisher (www.vdf.ethz.ch) or also via amazon Germany (www.amazon.de).
Cochlear Evanescent Liquid Sound-Pressure Waves Near Localized Oscillations of the Basilar Membrane.
Evanescent liquid sound-pressure waves (i.e., standing waves, of limited spatial extension, with variable pressure and liquid-particle velocity but negligible density variation) play a fairly important role, e.g., in a part of the models for the origin of spontaneous oto-acoustic emissions (SOAEs). The corresponding liquid sound-pressure function obeys the Laplace equation. These waves can be studied with the help of resonators such as tuning forks or drinking glasses. The free-oscillation frequency reductions caused by submerging the resonators in water amount to a semitone for tuning forks, and to more than an octave for completely submerged drinking glasses. These frequency reductions are shown to be mostly due to the kinetic energy of the evanescent waves generated by the resonators. A plausible liquid sound-pressure wave function near a localized oscillation of the basilar membrane (BM) of a cochlear box model can be found, e.g., by superimposing the waves generated by a miniaturized tuning-fork prong (prong radius 0.1 mm, prong axis oriented in y-direction and located at z = 0, x = 9.99, 10.00, or 10.01 mm), oscillating in z-direction; at time t = 0, the prong is momentarily at rest and has, in the three mentioned cases, a "vertical" displacement of -100 nm, +200 nm, and -100 nm. Analytic calculations of the lines of constant liquid sound-pressure amplitude, of the BM shape at time t = 0, and of the evanescent-wave streamlines (along which the liquid particles oscillate linearly) are described. A typical free BM oscillation frequency ratio (without-liquid / with-liquid) is shown to be 1.3, corresponding to about 0.4 octave. If such a BM oscillation generates a single-frequency SOAE, then the place of maximal oscillation amplitude is basal of the without-liquid BM resonance place for that frequency by 0.4 octave distance, i.e., by about 2 mm, so that the emission can be carried to the stapes by a "slow" travelling liquid-surface wave.
With best wishes,
Reinhart.
Reinhart Frosch,
Dr. phil. nat.,
CH-5200 Brugg.
reinifrosch@xxxxxxxxxx .