Acoustic Plane Wave Scattering from a Soft Finite Truncated Cone in Axial Irradiation

The axially-symmetric diffraction problem of the plane acoustic wave on the soft finite truncated cone is solved. The pertinent problem is formulated in spherical coordinate system as Dirichlet mixed boundary-value problem for Helmholtz equation, with respect to the scattered velocity potential. The diffracted field is obtained by the method of separation of variables as expansion in series of eigenfunctions for each of the regions formed by the cone. Making use of the continuity conditions of the total field and its normal derivative together with the orthogonality properties of the Legendre functions, the originally stated diffraction problem is reduced to the infinite system of linear algebraic equations (ISLAE). The main parts of the asymptotic expressions of diagonal matrix elements of this ISLAE, determined for large indexes, identify the convolution type operator. To perform an exact inversion of this operator the method of analytical regularization is used. As a result, the solution of the initial diffraction problem is reduced to ISLAE of the second kind. The numerical solution of this system relies on the reduction method and its accuracy depends on the truncation order. The low-frequency case of the problem is considered and the analytical solution in the explicit form is derived. Characteristic features of diffracted field as functions of cone's parameters are examined.