Acoustic diffraction by a material cone

The boundary-value problem for the Helmholtz equation connected with an infinite circular cone has been analyzed. The proposed scheme of solution includes application of the Kontorovich-Lebedev (KL) transform. The fields excited by a rotationally invariant ring source have been considered. Uncoupled singular integral equations (SIEs) satisfied by the spectral functions were derived. The singularities of the spectral functions were deduced. Some asymptotic approximation for the field with source or observation point near the tip of the cone was obtained. Alternative representations for the far fields were derived. The conditions of validity of the derived field representations for a given set of problem parameters were studied.