Sound transmission in a duct with a side-branch tube array mounted periodically

Abstract

This paper presents a theoretical study of sound propagation in a duct with a tube array flush-mounted periodically. The underlying wave interaction is analyzed by the transfer matrix method, and validated by the numerical simulation. With identical tubes, a particular situation is observed that the periodic distance and the tube length are “matched,” leading to a strong coupling effect by Bragg reflection and tube resonance, resulting in a wide stopband in low frequency. Even when the tubes in the array are not identical, the Bragg reflection can still work to broaden the stopband which was originally contributed by tube resonances.