This invention relates to a method and apparatus for the fundamental prediction, analysis, and parametric studies of the interaction of multiply scattered waves of any nature (acoustic, electromagnetic, elastic) with particulate composites (solid or fluid particulate phases included in a solid or fluid phase). It comprises of: a) a Prediction Engine 21 to predict the composite physical attributes from those of the constituent phases, b) an Inversion Engine 22 to estimate a subset of the attributes of the constituent phases and composite from the rest of those attributes, and c) an ergonomic Graphical Interface 23 to enable the user to easily set up complex simulation experiments for the analysis, and synthesis of real systems in which generic waves interact with composites. The Prediction Engine 22 is suitable for integration into existing acoustic or optical particle size analyzers to thereby extending their concentration ranges by at least two orders of magnitude.