Sound transmission in a slowly varying lined flow duct

Sound transmisslon through straight circular duels with a uniform (inviscid) mean flow and a constant acoustic lining (impedance wall) is classicaIly described by a modal expansion. A natural extansion for ducts with, in axial direction. slowly varying properties (Iike diameter. wall impedance, and mean flow) is a muttiple-scales solution. It is shown in the present paper that a consistent approximation ol boundary condition and mean flow allows the multiple-scales problem to have an exact soIution. Tuming points and other singularities of this soIulion are discussed.