Contributions to the Theory of Sound Propagation in Ducts with Bulk-reacting Lining

(Received 26 February 1984; accepted for publication 20 November 1984) A theoretical nalysis ofsound propagation in cylindrical ducts lined with porous material {bulk absorbers) is presented. Three configurations are discussed. (1) The porous material is homogeneous; thenthe sound field is built up of modes. (2) The properties of the liner vary slowly in an axial direction. A pure modal solution is, in general, not possible, but the field can be described bymod•s of the homogeneous liner, of which the amplitudes and wavenumbers vary in an axial direction slowly with the liner (multiple scale solution). (3) The porous material is embedded in an annular structure of partitions. For structural reasons this is a common situation. If the pitch of the partitions i small, the sound field in the liner is, per circumferential mode, decoupled from the duct field, and its effect can be described acoustically b an impedance (per circumferential mode}. This "quasi-point-reacting" boundary condition may be easily incorporated in calculation procedures for ducts with locally reacting lining.