Acoustic models

Researchers have developed impressive theoretical models for predicting acoustical properties of a wide range of materials . However Zorba uses a simple class of model in which the porosity is high, the frame or skeleton of the material is infinitely rigid, and the tortuosity of the material is not great. These models are applicable to a wide range of common materials, fibreglass, rockwool, polyester, wool, etc.

A fundamental assumption of Zorba is that most acoustic materials can be modelled as equivalent fluids with a complex density and complex compressibility which are functions of frequency. This is a good assumption for a wide range of common materials such as fibreglass, mineral fibre (sometimes called mineral wool), polyester fibres, wool, hessian fibres,and in fact most porous materials that have a porosity of greater than 90% and a reasonably rigid frame. Some materials that can not be accurately represented this way are polyurethane foams where the structure of the material can not be considered rigid, or low porosity materials such as closed cell foams or the ground or road pavements which might be only 10 to 30% porosity. For materials which have low porosity and high tortuosity (e.g. medium density wood chip board, acoustic plasters, wet felted mineral fibre) this model as it stands is not accurate. A model which is more accurate for these conditions is that developed by Wassilieff.

In architectural acoustics most common porous absorbers can be modelled well enough by the methods used by Zorba

Zorba provides a choice of models. In most cases you can just leave it on the default model which is a model published by Allard and Champoux in the Journal of the Acoustical Society of America Vol 91 (1992), "New Empirical equations for sound propagation in rigid framed porous materials". This is a good choice over a wide range of flow resistivities.

Possibly the most well known model is the phenomenological model of Delany and Bazley published in Applied Acoustics Vol 3 (1970) which has been widely used. It is however limited in the range of frequencies and flow resistivities that it can be used for.

Mechel published some corrections in Acustica Vol 35 (1976) which extended its frequency and flow resistivity range.

The models of Beranek and Rayleigh are early theoretical models which are not correct but are included for interests sake. For a range of flow resistivities and frequencies the absorption coefficients are not very sensitive to the choice of model.

An attractive model which uses the flow resistivity as the primary parameter, but includes an additional parameter called the shape factor (which for normal materials can be regarded as constant) was developed by Allard and Champoux. The arithmetic involved in calculating the propagation coefficients is more tedious than the Delany and Bazley model, but once built into a computer algorithm can thenceforth be ignored.

For room acoustics purposes it is desired to know the sound absorption coefficients as a function of frequency. The usual way of doing this is to first predict the characteristic impedance and complex propagation coefficient and then to derive the normal incidence absorption for a particular thickness and mounting arrangement .