Acoustical characteristics of rigid fibrous absorbents and granular materials

TLDR

A model is developed to predict the acoustical characteristics of rigid fibrous absorbents, soils, and sands using five parameters. The model employs porosity, flow resistivity, tortuosity, steady‑flow shape factor, and dynamic shape factor, requiring only porosity and flow resistivity plus a derived shape factor for practical use. The model shows that tortuosity correlates with porosity, proposes a simple shape‑factor relationship, and provides superior predictions to empirical formulas, especially for high‑flow‑resistivity soils and sands at low frequencies.

Abstract

A model is developed that predicts the acoustical characteristics of rigid fibrous absorbents soils and sands from five parameters. These parameters are porosity, flow resistivity, tortuosity, steady flow shape factor, and dynamic shape factor. Tortuosity is shown to be related simply to porosity and a simple relationship between the shape factors is postulated. In practice, therefore, only two measurable parameters (porosity and flow resistivity) are required together with a third shape factor parameter, appropriate values of which are deduced for the media of interest by comparison with appropriate measurements. The model is shown to give superior predictions to those of empirical formulae that use flow resistivity only, particularly when applied to high flow resistivity soils and sands at low frequencies such that the stated range of validity of the empirical formulae is exceeded.