Theoretical Acoustics

Objectives:

The objective of the course is to provide an introduction to principles and methods in theoretical acoustics/ultrasonics, with emphasis on physical mechanisms, laws, relationships, and relevant mathematical methods/models. The course shall convey an understanding of central mathematical methods in acoustics, in areas that are relevant in practical applications of acoustics and ultrasound, in gases, liquids, and solid media.

Contents:

The course gives a theoretically oriented extension of PHYS271 and addresses key methods and approaches that are important in practical applications of acoustics and ultrasonics. It addresses parts of the classical theory of diffraction and sound radiation, sound scattering from simple objects (spheres, bubbles) and volume scatterers, waveguides in homogeneous and inhomogeneous media, basic acoustic ray and normal mode theory, Kramers-Krönig causality relations in non-ideal fluids, basic tensor algebra, basic elasticity theory for isotropic and anisotropic solids, and linear sound propagation in elastic materials. The course constitutes a theoretical fundament for further studies in experimental and theoretical acoustics, within a number of application areas (such as marine acoustics, medical ultrasound, petroleum acoustics, piezoelectric transducers, finite element modelling (FEM) of sound propagation in solid media, etc.).

On completion of the course, the student shall have the following learning outcomes, defined in terms of knowledge, skills, and general expertise:

Knowledge:

• Explain key concepts, physical mechanisms and theoretical models for sound in gases and liquids: sound radiation, sound propagation in homogeneous and inhomogeneous media, diffraction, scattering, causality relations.
• Explain key concepts, physical mechanisms and theoretical models for sound in elastic media (solids): basic tensor algebra, basic elasticity theory for isotropic and anisotropic solid media, and linear sound propagation in elastic materials.

Skills:

• Use physical laws, relationships and mathematical methods to solve relatively advanced problems in acoustics.
• Use common mathematical models and metods for description of radiation and propagation of sound waves in gases, liquids, and solid media.

General expertise:

• The studenthas a good understanding of common approaches and theoretical methods used in acoustics / ultrasound, with emphasis on physical mechanisms, laws, relationships, and mathematical models/methods that are important in practical applications of acoustics and ultrasound, in gases, liquids, and solid media.