Near acoustic field of the finite rigid cone

Abstract

The canonical problem of diffraction of the plane acoustic wave from the finite hollow rigid cone in the case of axial incidence is solved. The diffraction problem is formulated as a Neumann boundary value problem for the Helmholtz equation. The diffracted field is sought in the terms of eigenfunctions of the Helmholtz equation taking into account the radiation condition and the edge condition. Making use of the mode matching technique and the orthogonality properties of the Legendre functions the pertinent problem is reduced to infinite system of linear algebraic equations (ISLAE). Analytical regularization procedure is used to effect the analytical inversion of a singular part of the diffraction operator and to reduce the initial problem to ISLAE of the second kind. The numerical solution of ISLAE relies on the reduction method and it accuracy depends on number of truncation. The validity of obtained results is confirmed by it comparison with those known for a circular rigid disc.