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Local basilar-membrane oscillations.

Dear colleagues,
Local standing basilar-membrane (BM) oscillations involving evanescent sound-pressure waves in the cochlear liquid above and below the BM may be possible after all, and thus may occur during single-ear tinnitus and during spontaneous oto-acoustic emissions. It is not necessary to postulate, in the usual cochlear box model, an exotic BM stiffness function S(x) such as that mentioned in my posting of May 2, 2011. Instead, S can be assumed to be locally place-independent. Newton's second law, applied to the BM elements, is fulfilled if a suitable (fairly small) additional force on the BM, generated by active outer hair cells (OHCs), is introduced. That force is local, too, and is in phase with the force due to the BM stiffness. Since work equals force times path, the time-averaged energy given to the BM by that additional force vanishes, as is reasonable for the treated friction-less oscillation.
The OHC force generating the "active" peak in cochlear travelling waves for frequencies above about 1 kHz, in contrast, is in phase with the BM oscillation velocity and so does feed energy into the wave. At frequencies of a few hundred Hz, however, the OHC-generated feedback at the best place is small (slightly positive or slightly negative), and so is similar to that in the above-mentioned hypothetical standing wave. 

Reinhart Frosch,
Dr. phil. nat.,
CH-5200 Brugg.
reinifrosch@xxxxxxxxxx .