Acoustic Scattering

Supervisor: Dr Harlen

Ultrasound spectroscopy and sonar rely on the scattering of sound waves at interfaces between different media. In sound waves the pressure, p, satisfies the linear wave equation

.

where c is the velocity of sound, which depends upon the properties of the media. For time harmonic acoustic waves of the form,

,

the wave amplitude u, satisfies the Helmholtz equation

where the wave number k=w/c. For simple shapes, such as spheres and cylinders solutions to the Helmholtz equation can be obtained using separation of variables.

The objectives of this project are to find how plane waves are scattered by simple shapes such as planes, cylinders and spheres, and to find how the form of the scattered wave depends upon the size and properties of the scatterer.

Pre-requisites

MATH 2370 Linear Differential Equations and Transforms

References:

W.C. Elmore and M.A. Heald, “Physics of Waves”, Dover

D.I. Jones “Acoustic and Electromagnetic Waves”, Oxford

R. Kress, Chapters 2.1 and 2.2 in Scattering: Scattering and Inverse Scattering in Pure and Applied Science (ed. Pike & Sabatier).