Abstract
In this paper, the transfer matrix method is used to study the dispersion of acoustic waves in a finite periodic expansion chambers system with a defect. Two kinds of structures are studied. The first one is formed by expansion chambers, which are symmetrical concerning a defect, and the second one is asymmetrical with a defect. Studying the properties of consistent peak (defective mode) at normal incidence is the objective of these calculations. Consistent peaks arise in the forbidden frequency intervals when a fault in the perfectly periodic structure is present. Concerning the defected asymmetrical configuration, there is a consistent peak located inside acoustic band gap. On the other hand, in the symmetrical structure, two consistent peaks appear in the band gap. In the asymmetrical structure, the consistent peak height depends on the variance in the cross-section of the defect guide. Moreover, the impact of the defect guide's length on the number of consistent peaks that appear in the band gap will be examined. These results can be used in several applications, such as the design of new kinds of acoustic filters.