Concept of Acoustical Backgrounds, Partial Wave Analysis and the Manifestation ofCertain Classes of Resonances as Standing Waves on Elastic Targets

摘要

In earlier work it was shown that certain classes of resonances excited onelastic solids correspond to standing wave patterns on the object surface. This observation was in fact implicit in the circumferential nature of such resonances made clear by the early theoretical work in quantum scattering physics, as well as the experimental work of R. Goodman, et. al. One can demonstrate the validity of the assumption that a scattering event can be divided into the resonance contribution and the non-resonance background contribution if one knows the correct background. The correct background was proposed in 1976 by Uberall, et. al. and the correct elastic shell background by Werby in 1998 in the recently published book on resonance scattering theory. We outline the rational for subtracting the appropriate acoustical background (in partial wave space) by either examining the partial wave function for each mode as a function of frequency or by examining a plot of all the partial waves as a function of mode number. This leads to unambiguous characterization of the resonances. Further we show that this way of dividing a problem into resonance and non-resonances components follows naturally from Hilbert-Schmitt theory even to the extent that one obtains the Breit-Wigner terms for the resonance components. Ultimately. this methodology leads to an unambiguous classification scheme for all orders of resonances and in addition allows one to isolate new phenomena such as water borne waves recently identified by French scientists. (AN).