Model and experiments of multiple acoustical scattering from small obstacles

Abstract

A self-consistent model is presented to calculate acoustical scattering of waves from many discrete obstacles, including multiple scattering. The model provides a formulation for incorporating single scattering Green’s functions into a multiple scattering solution using auxiliary sources. Geometry and material parameters of the scatterers in the ensemble may be different, and are arbitrary as long as each single scattering solution is known. In restricting the number of auxiliary sources the model is approximate, yet it is empirically shown to work in a quantitative manner for scatterers of ka up to about one, where k is the wave number of the background medium and a is half of the cross section of a scatterer. To ease experimental verification, a two-dimensional setup is considered where obstacles are circular cylinders of infinite length. The model is tested against experimental data gathered from ultrasonic experiments in a water tank. Ensembles of two to ten strong scattering cylinders were used, their radius being chosen such that ka =3D 0.5 at the mean frequency of the transducers. Numerical and experimental results are compared in time and frequency domain and show quantitative agreement in all investigated arrangements. Results of a numerical experiment including 50 different cylinders are also shown.