Sound propagation in ducts with spatially variant parameters

The one-dimensional theory of sound propagation in ducts is generalized and investigated in the paper. It can be assumed that any duct system consists of two kinds of elementary structures: One is the piped structure in which the characteristics, such as the acoustical parameter on the interior surface of the wall, the cross-section area of the duct and the aerodynamic parameters of the flow, etc., will vary continuously and slowly with distance along the axis of duct. The other is the local structure with discontinuity in which the characteristics will change abruptly. The acoustical properties of both structures are analysed in general cases based upon the fundamental equations of aerodynamics, and their transmission matrixes are derived and discussed respectively. Two typical examples are analysed and discussed.