Рассеяние звуковых волн на сферах: методы решения и основные характеристики (обзор)

Abstract

The investigation of the sound wave scattering phenomenon on small-sized inhomogeneities is important both for studying the fundamental nature of this phenomenon and from a practical point of view, since many applications of acoustic waves are based on scattering phenomenon, such as sonar, sounding of the atmosphere and ocean, nondestructive testing devices, creation of a positioned 3D sound, etc. In many systems under consideration, obstacles are spherical (or can be considered as such). Present review is devoted to the analysis of the main works on theoretical methods for solving problems of acoustic wave scattering on spheres and determining the main characteristics of this phenomenon, as well as on existing experimental works. Two theoretical approaches to solving the presented problem can be distinguished. In the first approach, it is assumed that the distribution of scatterers is random, and the average value of the scattered field is calculated. In the second approach, which is given the main attention in this paper, the solution is reduced to large system of integral or linear algebraic equations using various methods, such as the T-matrix method, addition theorems for spherical functions, Green’s functions, integral equations. The first approach allows one to consider systems with a large number of randomly distributed particles, however, due to the averaging of the sound field, it is impossible to determine the pressure at a specific point in space. The second approach makes it possible to determine the zones of increasing and decreasing pressure, however, for a large number of spheres, the solution requires significant computing resources and processor time. The analysis of scientific papers that define the main characteristics of the scattering phenomenon, such as the total or back scattering cross-section, has shown that analytical formulas and numerical studies are limited to the cases of a single sphere or systems with two spheres. Thus the problem of determining the formulae for these characteristics in the general case remains unsolved and is relevant.