A family of exact transient solutions for acoustic wave propagation in inhomogeneous, non-uniform area ducts

This paper presents a family of exact solutions for quasi-one-dimensional, transient acoustic wave propagation in ducts with mean temperature and area variations in the absence of mean flow. These solutions are obtained using a transformation of the spatial and acoustic variables in a manner suggest ed by the WKB approximation. Exact travelling wave-type solutions are obtai ned for a class of temperature and area profiles. These solutions differ fr om the classical travelling wave solution, however, in that the acoustic pr essure and velocity are not algebraically related by the local value of the acoustic impedance, (p) over bar (x)(c) over bar (x). Although these solut ions resemble the approximate, "high frequency", WKB form of solution of th e wave equation, they have the interesting property that they are exact, re gardless of the scale of the acoustic disturbance relative to that of the i nhomogeneity. (C) 2001 Academic Press.