Total scattering cross-section of a nondeformable sphere partially insonified at a circular annular spot

The axisymmetric problem of scattering of a finite sound beam with an annular cross-section by an acoustically soft or immovable rigid sphere immersed in a fluid medium is considered. The pressure in the incident quasi-plane wave is represented in terms of the partial impact parameters by the superposition of the spherical harmonics with the Lorentz multipole resonance distribution. The analysis of the total scattering cross-section vs frequency and wave beam parameters is performed. It is shown that a high-resolution of the total scattering cross-section resonances corresponding to the Franz creeping waves is achieved when the base rays of the incident wave are grazed on the sphere and the beam is narrowing. The particularities of these resonances are considered for the case of soft and rigid spheres.