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Re: Laws of physics and old history...

At 11:00 AM -0500 11/10/11, Ranjit Randhawa wrote:
Dear Dick,
I came across these auditory patterns due to pure tones in a text book on Physics where these figures have been attributed "courtesy of Dr. Harvey Fletcher". Ref: Mechanics, Heat and Sound by Francis Weston Sears, Library of Congress card No. 51-899, Addison-Wesley Publishing Company, Inc., Second Edition, Seventh printing-June 1958 (pretty long ago!). I don't have the history on how Fletcher derived these figures. I have over the years have thought about these figures with the results of ISI statistics and came to the conclusion that the only way a result such as shown in these figures could be explained is by showing that it was possible to describe a frequency analysis method that analyzes a pure tone as sum of a harmonic series in the energy domain. But that is neither here or there, it was simply my approach.

Sorry for the delay. I got the Sears textbook so I could see what you're referring to. The figures are from Fletcher's 1940 "Auditory Patterns" paper (I can provide a copy on request). You're right that Fletcher does show a cochlear response pattern that includes responses at what he calls "subjective harmonics". He gets these by measuring the masking effect of pure tones on other tone frequencies, and assumes that masking is proportional to the response in the cochlea at a place that responds to the fundamental of the probe frequency. A slightly unusual idea, but not bad as a simplifying assumption for its time.

No objective correlate in the form of a space pattern of mechanical or neural response with harmonic bumps along the length of the cochlea has ever been seen, as far as I know. If you want to consider a time-domain mechanism to explain the masking patterns, you can do that in the neural domain, based on the neural activity patterns out of the quasi-linear cochlea. That's where the inter-spike interval stuff can apply.

I don't quite understand the term "volume compliance", and am quite happy to accept that not much of a change of BM geometry is required to provide the required change of volume range for a TW, but was more concerned with the restoring force available from the BM, and hence "stiffness", I guess I could have called it "springiness?". This does not vary as much as required, at least as reported.

Compliance is the inverse of stiffness; volume compliance, sometimes written "(volume) compliance", is in the sort of dimensions that works easily in a fluid problem: volume of fluid displaced per unit pressure.

In the case of the basilar membrane, it's the volume of fluid displaced via membrane displacement, per unit length of cochlear duct, per unit of pressure difference across the membrane; or the BM is characterized by its local volume compliance per unit length. Maybe with the "per unit length" in there it's not exactly the same thing as used in characterizing blood vessels and lungs and such in the medical field (see for example this book: http://books.google.com/books?id=fqWIm8RmVYsC&pg=PA59 and this one http://books.google.com/books?id=i5Y6vrWlnXkC&pg=PA31 ). But it's a bit different from simple mechanical "compliance", which is just displacement per force. In any case, I didn't really mean anything significantly different from "stiffness" as usually interpreted in the cochlea, but that term is too ambiguous as it might be that in the factor-of-6 interpretation it was stiffness as resistance to bending, without considering the membrane width.

Bottom line is that "springiness" does vary enough to explain the wide range of traveling wave velocities.