Determination of the distributed parameters of a lossless wave supporting system from boundary measurements

Abstract

A lossless wave supporting system is modelled by two linear partial differential equations with variable coefficientsα(x) andβ(x),x≥0, which represent the distributed parameters of the system. The problem of determiningα(x) andβ(x) from measurements performed at the boundaryx=0 is considered. It is shown that generally it is only possible to determine an impedance function$\bar Z$(ξ), where$\bar Z$ and ξ depend onα andβ. If some additional relationship is known betweenα andβ, however, it may be possible to fully determine these parameters. This is the case if, for example, it is known that the wave speed is constant. The results are interpreted for sample cases from solid mechanics, fluid mechanics, acoustics, and electromagnetic theory, and solutions are given of specific problems. The paper generalizes work on determination of vocal tract shapes from acoustical measurements made at the lips.