The application of reciprocity theory to scattering of acoustic waves by flaws

Abstract

The reciprocity theorem and the scattering matrix formalism of electromagnetic theory have been adapted to obtain formulas for scattering of acoustic waves from flaws. The technique has been applied, in the Born approximation, to determine scattering of plane waves by small flaws, and with an elastostatic approximation to find the scattering from a flat elliptical crack. A third example is a treatment of the optical approximation to scattering from a curved interface between two media. In all cases results are obtained which are applicable for flaws placed either in the Fresnel region or Fraunöfer region of unfocused transducers, or near the focal point of a focused transducer. A fourth example, given in the Appendix, uses the reciprocity theory to derive the axial field of a piston transducer in contact with the surface of a solid.