Investigation of acoustic scattering from a pair soundproof spheres under external influence

A mathematical model extension is presented and numerical studies were made for the problem of acoustic scattering from two soundproof spheres (the case of hard spheres) with an arbitrary acoustic impedance under the action a spherical wave from a monopole radiation source arbitrarily located in space. The case of two spheres is of practical interest, since, on the one hand, the scattered fields from the spheres interact with each other, and on the other hand, the interaction is simple enough for it to be studied in detail. When solving the Helmholtz equations, a numerical technique based on the fast multipole method is used, which allows to achieve high accuracy of the results obtained with minimal computer time. The testing of the algorithm was carried out on the basis of the known data (from the literature) of the response on the surface of one of the spheres in the case when the axis connecting the monopole radiation source and the center of the first sphere is perpendicular to the axis connecting the centers of the two spheres. The pressure distribution around the spheres is investigated for different values of the distance between the centers of the spheres and the arbitrary location of the monopole radiation source in space. It is shown that with certain parameters of the system, the presence of a second sphere can lead to the appearance of an increase or decrease zone of pressure. The obtained results will further allow generalizations of the mathematical model to the cases of acoustic scattering from a pair of sound-permeable spheres (cases of gas bubbles or liquid droplets) and many spheres (both coaxially and arbitrarily arranged in space), and can also be used for test calculations during verification numerical solution of these generalized problems.