A transfer matrix approach for characterizing horn-like spiraling acoustic metamaterials and other complex spherically symmetric objects

A common method for characterizing acoustic materials such as porous absorbers or metamaterials is the four-microphone method. This measurement procedure acquires the acoustical properties of a material using a transfer matrix. Generally, the transfer matrix is based on plane wave propagation, limiting it to 1-D material characterization. However, in some cases it is desirable to characterize a material based on spherical coordinates. For example, this report presents a spherically spiraling acoustic metamaterial that cannot be subjected to the traditional plane wave transfer matrix method. Accordingly, the four-microphone method for spherically symmetric materials is derived to obtain the necessary acoustic properties of the metamaterial. First, the analysis for the transfer matrix based on the spherically symmetric wave equation will be presented and then implemented in both simulation and measurement. The utility of this characterization streamlines efficient application in simulation and optimization processes to design more complicated spherical acoustic metamaterials that can be incorporated with electroacoustic devices like loudspeakers. This methodology delivers new possibilities for classifying acoustic properties of objects subjected to a spherically propagating wave such as horns and spherical acoustic metamaterials.