Acoustic performance of Herschel-Quincke tubes with gradually variable cross-section ducts

The Herschel-Quincke Duct is the simplest implementation of the interference principle with attenuation purposes. Its acoustic behaviour is well known, and it is characterized by the presence of relatively narrow attenuation spikes which, depending on the precise geometrical definition, may give rise to an acceptable attenuation in wide frequency bands. Apart from the study of the influence of a mean flow on its acoustic performance, different modifications to the basic Herschel-Quincke tube have been previously explored, such as the consideration of multiple interfering paths, or the inclusion of a duct connecting the two main propagating paths in the basic configuration. In this paper, a different modification is considered, in which one of the ducts in the two-duct configuration does not have a constant cross-section. A one-dimensional linear model for this modified device incorporating mean flow effects is developed, which is subsequently used to explore the potential of the proposed configuration in order to improve the attenuation characteristics of the Herschel-Quincke tube.