Scattering of acoustic waves by rigid cylindrical objects with sharp corners

Abstract

The T-matrix or Null Field approach is employed for studying scattering of acoustic waves by rigid cylindrical obstacles with sharp corners. A piecewise basis function is used to represent the surface field. The algebraic system of equations obtained from the resulting integral equations is solved for computing the surface and farfield amplitudes. Numerical results are presented for backscattering and bistatic scattering cross sections for square and intersecting circular cross sections and are compared with those obtained for smooth cross section, such as elliptical cross sections. Wavelengths down to one fifth of the maximum dimension of the section are considered. This frequency range is wide enough to definitively conclude that the dominate effect for objects with sharp corners is the interference of waves specularly reflected at such points also known as flash points. For smooth shapes such as the ellipse, the dominant effect is that of creeping waves. Schlieren photographs of a pulse propagating into the shadow of a cylinder with square cross sections are also given.