The problem of diffraction of a plane acoustic wave by a finite soft (rigid) cone is investigated. This\none is formulated as a mixed boundary value problem for the three-dimensional Helmholtz equation\nwith Dirichlet (Neumann) boundary condition on the cone surface. The diffracted field is\nsought as expansion of unknown velocity potential in series of eigenfunctions for each region of\nthe existence of sound pressure. The solution of the problem then is reduced to the infinite set of\nlinear algebraic equations (ISLAE) of the first kind by means of mode matching technique and orthogonality\nproperties of the Legendre functions. The main part of asymptotic of ISLAE matrix\nelement determined for large indexes identifies the convolution type operator amenable to explicit\ninversion. This analytical treatment allows one to transform the initial diffraction problem into\nthe ISLAE of the second kind that can be readily solved by the reduction method with desired accuracy\ndepending on a number of truncation. All these determine the analytical regularization\nmethod for solution of wave diffraction problems for conical scatterers. The boundary transition\nto soft (rigid) disc is considered. The directivity factors, scattering cross sections, and far-field diffraction\npatterns are investigated in both soft and rigid cases whereas the main attention in the\nnear-field is focused on the rigid case. The numerically obtained results are compared with those\nknown for the disc.
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