Experimental Determination of a Reflective Muffler Scattering Matrix for Single-Mode Excitation

The aim of the paper is to experimentally determine the scattering matrix S of an example reflective muffler of cylindrical geometry for Helmholtz number exceeding the plane wave propagation. Determining the scattering matrix of an acoustic systems is a new and increasingly used approach in the assessment of reduction of noise propagating inside duct-like elements of heating, ventilation and air conditioning systems (HVAC). The scattering matrix of an acoustic system provides all necessary information on the propagation of wave through it. In case of the analysed reflective silencer, considered as a two-port system, the noise reduction was determined by calculating the transmission loss parameter (TL) based on the scattering matrix (S). Measurements were carried out in two planes of the cross-section of pipes connected to the muffler. The paper presents results of the scattering matrix evaluation for the wave composed of the plane wave (mode (0,0)) and the first radial mode (0,1), each of which was generated separately using the self-designed and constructed single-mode generator. The gain of proceeding measurements for single modes stems from the fact that theoretically, calculation of the S-matrix does not require, as will be presented in the paper, calculation of the measurement data inverse matrix. Moreover, if single mode sound fields are well determined, it ensures error minimization. The presented measurement results refer to an example of a duct like system with a reflective muffler for which the scattering matrix S was determined. The acoustic phenomena inside such a system can be scaled by the parameter ka.