An improved multimodal method for measuring the equivalent acoustical properties of porous materials

This paper extends the original multimodal method to extract the complex wave number and characteristic impedance of porous materials beyond the cut-off frequency from an arbitrary mode rather than only a plane wave component. Four modifications are implemented to enhance both low- and high-frequency measurement accuracy, and wave number formulas are modified to include tube attenuation effects. Validation experiments for an air column and a polyurethane foam sample are conducted in an 8× 8 cm² rectangular impedance tube, with parallel measurements using the standard four-microphone approach in a 3-cm-diameter circular tube. The experimental results demonstrate that the improved multimodal method can accurately determine equivalent acoustical properties of porous materials up to nearly three times the cut-off frequency and at low frequencies, the accuracy is enhanced at the same time.