An extension of the transfer matrix method to analyzing acoustic resonators with gradually varying cross-sectional area

Abstract

The transfer matrix method was used to analyze the acoustical properties of stepped acoustic resonator in the previous paper. The present paper extends the application of the transfer matrix method to analyzing acoustic resonators with gradually varying cross-sectional area. The transfer matrices and the resonant conditions are derived for acoustic resonators with four different kinds of gradually varying geometric shape: tapered, trigonometric, exponential and hyperbolic. Based on the derived transfer matrices, the acoustic properties of these resonators are derived, including the resonant frequency, phase and radiation impedance. Compared with other analytical methods based on the wave equation and boundary conditions, the transfer matrix method is simple to implement and convenient for computation.