Derivation of an Acoustic Two-Port Scattering Matrix for a Multimode Wave Applying the Single-Mode Generator

The paper presents the procedure of experimental derivation of an acoustic two-port scattering matrix for a multimode wave propagating, for example, in a muffler of a complicated design, applying the single-mode generator. The self-designed single-mode generator is constructed in the form of a matrix of acoustic monopoles and is capable to generate a selected single mode. The scattering matrix formalism is a new approach to analyse the acoustical systems containing one or more duct-like elements (joints) connected by some undefined elements such as, for example, acoustic mufflers of different types and so the formalism is frequently applied to analyse the phenomena of noise reduction in such systems. Experimental derivation of the scattering matrix for a wave composed of N modes demands, in general, excitation of N different sound fields at each side of the two-port first. Finally the matrix composed of the modal pressures measurements obtained for each of the exited fields must be inversed to obtain the scattering matrix. Generating single N modes the matrix of the incoming pressure data is, theoretically, diagonal which makes derivation of the scattering matrix much easier. Generation of independent sound fields in the shape of single modes ensures the matrix to be well conditioned.