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 Her schel-Quincke tube side-branch configuration to adaptively attenuate the pr opagation of plane wave disturbances along a duct. Through the use of an ac tive membrane or piston element within the tube, the transmission loss char acteristics of the tube apparatus can be made to adapt to changes in the di sturbance frequency. This permits tracking of tonal disturbances over a wid e bandwidth in order to maintain optimal attenuation. The theory for an ada ptive Herschel-Quincke tube is presented, and the corresponding transmissio n loss is derived and given in terms of the tube geometry, piston mass, sti ffness and damping. As an illustrative example, analytical results are pres ented using a PVDF membrane as an equivalent piston. The derivation of the equivalent piston mass and stiffness of the membrane as a function of appli ed voltage is also presented. Analytical results illustrate how the transmi ssion loss of the adaptive Herschel-Quincke tube can be varied as a functio n of the voltage applied to the membrane in order to track changes in the d isturbance.