An extended transfer matrix method for measuring acoustical properties of porous materials beyond the cut-off frequency

In the field of measuring the complex wave number and characteristic impedance of porous materials, available impedance tube approaches assume that only plane wave is propagating such that the maximum frequency is limited below the cut-off frequency of the first higher order mode. This indicates that if measurements at higher frequencies are required, the tube size has to be reduced, as well as the size of porous material sample, which may cause inaccurate results due to tube attenuation and edge-constraint effects. Through simulations, this paper presents an extended transfer matrix method to remove the plane wave assumption based on the fact that the propagation of plane wave through the porous sample can be characterized by the same transfer matrix whether higher order modes exist or not. This method arranges measuring points upstream and downstream the sample for implementing mode decomposition to extract the transfer matrix for plane wave in a multi-modal field. From the matrix elements, the complex wave number and characteristic impedance are determined in the same way as the original transfer matrix method. Based on numerical simulations and the Monte Carlo approach, the method effectiveness and a suitable measuring points layout are studied in this paper.