Acoustic Propagation in Ducts with Varying Cross Sections

Abstract

The method of multiple scales was used to derive the equations that describe the spatial and temporal variation of the amplitudes and phases of acoustic modes propagating in slowly varying hard-walled or lined ducts. The analysis was carried out for rectangular as well as circular ducts. These equations were also derived from the conservation of energy. For large-admittance or high-frequency modes, an approximate expression was obtained for the attenuation. This expression shows that all possible acoustic modes are attenuating. The results also show that varying the cross-sectional area can lead to elimination of some of the acoustic modes.