Fuzzier but simpler analytic models for physical acoustics and structural acoustics

Abstract

Acousticians have long been forced to analyze physical systems for which they apparently do not have enough information to make detailed analytical or computational predictions. One could say that their knowledge of such systems is ‘‘fuzzy.’’ Alternately, the means of measuring the details or of describing such a system may be in principle possible, but the answers one really desires, those which one can ‘‘deal with,’’ are of seemingly far less complexity than the modeled system in all its detail. The trick, of course, is to hypothesize a small number of simple and relevant descriptors of the system and to build a predictive model that uses only these descriptors. The rich and venerable literature of acoustics abounds with successful attempts in this vein, and a few such, taken from diverse subfields such as physical acoustics, architectural acoustics, underwater acoustics, and structural acoustics, are briefly reviewed in this talk. New problems and new questions lead to new searches for appropriate descriptors and for simple models which employ these descriptors. Theoretical tools which help to fill in the gaps caused by the incompleteness of these descriptors are general conservation principles and Jayne’s theory of maximum-likelihood based on Shannon’s uncertainty function.