An Adaptive Herschel-Quincke Tube

Acoustic side branches and mufflers are commonly used to attenuate harmonic disturbances in ducts. This work introduces a variation to the classic Herschel-Quincke tube side-branch configuration to adaptively attenuate the propagation of plane wave disturbances along a duct. Through the use of an active membrane or piston element within the tube, the transmission loss characteristics of the tube apparatus can be made to adapt to changes in the disturbance frequency. This permits tracking of tonal disturbances over a wide bandwidth in order to maintain optimal attenuation. The theory for an adaptive Herschel-Quincke tube is presented, and the corresponding transmission loss is derived and given in terms of the tube geometry, piston mass, stiffness and damping. As an illustrative example, analytical results are presented using a PVDF membrane as an equivalent piston. The derivation of the equivalent piston mass and stiffness of the membrane as a function of applied voltage is also presented. Analytical results illustrate how the transmission loss of the adaptive Herschel-Quincke tube can be varied as a function of the voltage applied to the membrane in order to track changes in the disturbance.