Guy V. Norton
Naval Res. Lab., Stennis Space Center, MS 39529-5004
Jorge C. Novarini
Planning Systems, Inc., Slidell, LA 70458
The classical problem of sound scattering from an infinitesimal thin disk is re-examined in the time domain via Fourier synthesis of solutions calculated, in the frequency domain, through a T-matrix formalism. Two T matrices were used. The first was specifically developed for the disk, the second was more general in that it allowed a sphere to be transposed into an oblate spheriod, where in the limit that the length of the semi-minor axis goes to zero produces an infinitesimal thin disk. At difference from the frequency domain, once the solution is mapped onto the time domain, diffracted and reflected components of the scattered field are clearly separated. In this work this feature is used to analyze the relative strength of the different component of the impulse response, for the case of an acoustically rigid disk (Neumann boundary condition), and an acoustically soft disk (Dirichlet boundary condition). A point source is assumed, and the analysis is restricted to normal incidence. Results are compared with predictions from a Helmholtz--Kirchhoff solution. The main findings are that, while the reflected components of the hard and soft disks differ only in their sign (as predicted by Kirchhoff theory), the relative strengths of diffractions and reflections are drastically different for the two cases. Furthermore, for the hard disk secondary diffraction is clearly identified in terms of Huygens contributions, while no counterpart is observed for the soft disk. In addition, results from the oblate spheroid approaching the disk will be shown.