Acoustical analysis of multiple cavities connected by necks in series with a consideration of evanescent waves

In this paper, a new analytical method was developed to obtain the natural frequencies and natural modes of multiple cavities connected by necks or slits in series, which strongly affect the longitudinal acoustic modes. At the interface between a cavity and a neck, discontinuity in the cross-sectional area generates an evanescent wave in addition to a plane wave. The evanescent wave with a set of cross-modes decays along a distance from the neck, but the evanescent wave forces length correction term to be added to the characteristic equation of the enclosure. Therefore, the effective length, instead of the physical length of the neck, is used in the characteristic equation. We examined the validity of the proposed method by using finite element analysis for five cases. We also investigated the effect of changing the neck's position on the acoustical characteristics and the relation between added length and natural frequency.