Predicting the sound absorption of natural materials: Best-fit inverse laws for the acoustic impedance and the propagation constant

Natural materials are becoming a valid option for sound absorption treatments. In particular, among them, natural fibers have received increasing attention given their good thermal insulation properties, lack of harmful effects on health, and availability in large quantities. This paper discusses an inverse method to predict the acoustical properties of nine natural fibers. Six vegetative fibers: kenaf, wood, hemp, coconut, straw, and cane; one animal fiber, sheep wool; recycled cardboard; and granular cork are investigated. The absorption coefficient and the flow resistance for samples of different thickness have been measured. Moving from the Delany-Bazley model, this study compares the impedance tube results with the theoretically predicted ones. Then, using a least-square fit procedure based on the Nelder-Mead method, the coefficients that best predict both the acoustic impedance and the propagation constant laws are calculated. The inverse approach used in this paper allows to determine different physical parameters and to obtain formulas to include the investigated natural fibers in software modelling for room acoustics applications.