Pb. Subrahmanyam et al., A family of exact transient solutions for acoustic wave propagation in inhomogeneous, non-uniform area ducts, J SOUND VIB, 240(4), 2001, pp. 705-715
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.