Further investigations of empirical improvements to the Johnson–Champoux–Allard model

Abstract

Non-acoustical physical parameters (tortuosity, viscous characteristic length, thermal characteristic length, porosity and flow resistivity) of glass fibre, melamine foam, compressed melamine foam and reticulated polyurethane foam materials have been measured. Also tortuosity and two characteristic lengths have been deduced from impedance tube measurements using commercial software (Foam-X). Between 200Hz and 5kHz sound velocities in the materials have been deduced from impedance tube measurements. Between 79kHz and 1MHz they have been deduced from ultrasonic measurements.Predictions of sound velocities based on the Johnson–Champoux–Allard (JCA) model using measured non-acoustical physical parameters and, at high frequency, using ultrasonically-measured non-acoustical physical parameters (tortuosity, viscous characteristic length and thermal characteristic length) are found to be in good agreement with the ultrasonically-measured sound velocities above 100kHz thereby confirming the accuracy of the JCA model at ultrasonic frequencies.Differences in values of the two characteristic lengths between the Foam-X outputs and the results of ultrasonic measurements, using the slope method, and the important role of two correction factors in Kino’s empirical modification of the JCA model are explored in detail. It is shown that the values of characteristic lengths required to fit data using the original JCA model in the audible frequency range differ significantly from the ultrasonically-measured values. However it is shown that the Foam-X and the Kino model methods yield similar values for the two characteristic lengths in the audible frequency range. Further modifications of the JCA model to make it valid over a wider frequency range are proposed.