Engineering and the Environment, University of Southampton

Knowledge and understanding
Having successfully completed the module, you will be able to demonstrate knowledge and understanding of:

• Basic source models in acoustics, including monopole, dipole and higher order mutlipole sources.
• Inhomogeneous wave equations and methods for their solution, including Green's function techniques.
• Integral equation formulations for describing acoustic fields.
• The basic principles underlying analysis of the generation of sound by unsteady flow.
• The acoustics of enclosed sound fields at low frequency, including analytical models based on the assumption of light damping.
• Green's functions for sound propagation in ducts and wave guides.
• A range of numerical modelling techniques for the solution of the acoustic wave equation based on Finite Element and Boundary Element analysis.
• The use of these techniques through engineering software packages.
• The mathematics of Finite Element and Boundary Element methods which is critical to their correct use in practice.
• The interpretation of the results of numerical models.

Cognitive (thinking) skills
Having successfully completed the module, you will be able to:

• Read, understand and interpret the literature relating to analytical and numerical methods in acoustics.
• Recognise and select appropriate techniques for the solution of analytical and numerical problems in acoustics.

Practical, subject specific skills
Having sucessfully completed the module, you will be able to:

• Prepare data for commercial FE and/or BE codes to solve problems in acoustics to carry out design calculations on simplified model systems.

Key transferable skills
Having successfully completed the module, you will be better able to:

• Acquire a working knowledge of software packages for acoustic computations.

The aims of this module are to:

• Provide a general introduction to analytical and numerical techniques in acoustics.

• To introduce the student to the formal analytical basis for the solution of complex problems in acoustics.
• To describe numerical techniques available for the solution of problems in acoustics when analytical methods provide no means of solution.
• To give the student direct experience of the use of computer software which employs numerical methods for the solution of problems.

The Fundamental equations of acoustics

• Continuity of mass and momentum.
• The acoustic wave equation.
• Time harmonic solutions.
• Plane and spherical wave solutions.

Multipole Sources

• The point monopole source.
• The point dipole source; vector dipole strength.
• Longitudinal and lateral quadrupole sources.

The Inhomogeneous Wave Equation and its Solution

• The Green function. Principle of reciprocity.
• Solution of the inhomogeneous Helmholtz equation.
• The Kirchoff-Helmholtz integral equation.
• Implications for the active control of sound and radiation from arbitrary vibrating bodies.

Introduction to Aeroacoustics

• Lighthill’s acoustic analogy.
• Scaling laws for jet noise.

Enclosed Sound Fields

• The Green function for a rigid walled enclosure.
• Eigenfunctions and eigenvalues.
• Solution to the inhomogeneous Helmholtz equation; Light damping assumption.

Sound in Ducts

• Duct modes.
• Cut off frequency, phase speed.
• Green function for an infinite hard walled duct.

Introduction to Acoustic Finite Element Analysis

• Variational formulation for the wave equation.
• Finite Element discretization.
• Normal modes of irregular-shaped cavities with acoustically hard walls.
• Finite Element solutions for 2D and 3D interior problems.
• Finite Element solutions for unhanded problems.

Introduction to Boundary Element Methods

• Boundary Integral form of the reduced wave equation
• Direct collocation method.
• Application to cavity acoustics.
• Application to acoustic radiation. Non-uniqueness problems.

3 lectures a week.

Computing laboratories using proprietary engineering software packages to solve acoustic problems. The typical lab class size is 20. The instructor assists the students to work through tutorials and to attempt a novel analysis. Feedback is given by advice and assistance in the laboratory session.

Students join the course with widely varying experience of using such packages and this is dealt with by proportionate assistance during the computing laboratory sessions.

Students need to work in their own time to complete the laboratory work and are able to go to the lecturers for assistance.

Working on a formal assignment which is based on an example given in the laboratory, reading a set paper in the literature and then using the software provided to replicate the results. The assignment includes some development of the formulation they have used. Example sheets are provided to students in order to practise their analytical skills and these are backed up with interactive tutorial sessions. Students are encouraged to read supporting texts and a booklist is provided.

Secondary text

Acoustics - An Introduction to its Physical Principles and Applications
2nd Edition, 1989 (+ solutions)
1st Edition, 1981, A D Pierce, ASA


0883186128
McGraw-Hill
0070499616

Theoretical Acoustics
2nd Edition, 1986
1st Edition, 1968
, P M Morse
K U Ingård, Princeton UP 0691024014
McGraw-Hill
(no ISBN)

Active Control of Sound,
1992, P A Nelson
S J Elliott, Academic Press
0125154259

Boundary Element Acoustics Fundamentals and Computer Codes, T W Wu (ed), WIT Press (Southampton)
1-85312-570-9

Advanced Applications in Acoustics, Noise and Vibration, F J Fahy
J G Walker, Spon Press (London)
0415237297