Abstract

The Sommerfeld problem of acoustic scattering off a semi-infinite plate of vanishing thickness is a classic and well-studied canonical problem in diffraction theory. However, one key limitation of this problem is the clearly unphysical condition that the plate is of zero thickness. Jones sought to rectify this shortcoming in his seminal paper (1953) in which an analysis of a plate of finite thickness d is undertaken, using an approach analogous to the Wiener–Hopf technique. Crighton and Leppington considered the low-frequency regime of the same problem in their paper (1973) which yields a singular perturbation problem. This enables the use of matched asymptotic expansions, along with the Wiener–Hopf technique, to extract an expression for the far-field scattering valid for low-frequency waves.

Current work with Raphael Assier (Manchester) and David Abrahams (Cambridge) achieves the determination of an expression for far-field scattering which is valid for all frequencies, an important generalisation of previous work. This is done through application of various methods such as exploitation of symmetry inherent in the problem, the Wiener–Hopf technique and pole removal.

In the talk we will discuss key points of the solution procedure. The nature of the scattering potential will also be discussed, along with details of current numerical investigations.