Acoustic wave blocking in a duct with a chirped periodic wall

An analysis of sound waves in a circular cylindrical duct having a geometric periodicity at its wall is presented. The duct acts as a wave blocker preventing certain mode(s) from transmission under a specific resonance condition. When a chirp is imposed on the wall periodicity, the reflectivity spectra change. Various types of linear chirps are found to produce different frequency responses with features such as widening the no pass frequency band(s) or shifting them up or down over the frequency domain of interest. A perturbation method is used to derive the coupled-mode equations, which are solved numerically. The performance of the duct as a wave blocker is presented in terms of reflectivity spectra.