The Propagation of Sound in Cylindrical Ducts with Mean Flow and Bulk-reacting Lining I. Modes in an Infinite Duct

A theoretical model is presented for the propagation of acoustic waves in a cylindrical duct with bulk-reacting lining, consisting of sound-absorbing material behind a perforate. The model incorporates a uniform flow of the gas. We perform a modal analysis and attenuation curves are shown. In calculating the causally correct solution it is found that there is essentially only one convective instability wave—the so-called amplifying mode. For some combinations of parameter values an absolute instability may occur. Figures are presented which illustrate when this instability exists.