Exact solution for sound propagation in ducts with an axial mean temperature gradient and particulate damping

An exact solution for one-dimensional sound propagation in ducts in the pre sence of axial mean temperature gradient and particulate damping is present ed in this paper. The acoustic wave equation is derived starting from the o ne-dimensional momentum:and energy equation. The application of appropriate transformations leads to an analytically solvable Whittaker's differential equation for the case of a linear mean temperature gradient and Bessel's d ifferential equation for the case of an exponential mean temperature gradie nt. The derived analytical solutions are used to investigate the dependence of the acoustic field in a duct on temperature gradient and particulate da mping. (C) 1999 Acoustical Society of America. [S0001-4966(99)02211-0].