The University of Southampton
Courses

# ISVR3072 Mathematical methods for acoustics

## Module Overview

Mathematical methods for acoustics builds on the basic elements of acoustics covered in the core modules Acoustics 1 and 2, by introducing more advanced topics in theoretical acoustics. The focus will be on modelling sound fields generated by complex source distributions, including sound in enclosures and ducts. More sophisticated analytical methods will be introduced, including the acoustic Green function and integral solutions of the acoustic wave equation.

### Aims and Objectives

#### Learning Outcomes

##### Knowledge and Understanding

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

• More advanced concepts associated with modelling sound fields generated by complex source distributions.
• Theoretical models to describe the sound field produced by acoustic sources in enclosures or ducts.
• Integral solutions of the inhomogeneous Helmholtz equation, using the acoustic Green function.
##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Explain more advanced concepts in theoretical acoustics, such as the link between acoustic sources and acoustics modes of enclosures and ducts.
• Appreciate how to formulate solutions to predict sound fields generated by complex source distributions.
• Demonstrate how to use more advanced analytical methods in theoretical acoustics.
##### Transferable and Generic Skills

Having successfully completed this module you will be able to:

• Reading, understanding and interpreting scientific texts and papers.
• Critical analysis and evaluation.
• Communication of technical material in written reports.
##### Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Apply advanced mathematical methods for solving partial differential equations.
• Solve examples of practical problems in physical acoustics.

### Syllabus

Indicative content: • Mathematical methods for acoustics (vector calculus, generalised functions, Fourier analysis, Green functions and theory) - Revision of fluid dynamics and acoustics - Monopoles, dipoles and quadrupoles - Inhomogeneous wave and Helmholtz equations - The acoustic Green function - Integral solutions of the inhomogeneous Helmholtz equation - Sound in enclosures - Sound in ducts - A range of examples/applications in physical acoustics

### Learning and Teaching

#### Teaching and learning methods

The course will be delivered using a mixture of interactive lecture/tutorial sessions (in total three per week). Problems and solutions will be provided. Also, a formative assignment which will include mathematical analysis, numerical computation, and critical evaluation of the results, is included in the teaching and learning experience.

TypeHours
Tutorial12
Lecture24
Preparation for scheduled sessions24
Revision34
Follow-up work24
Total study time150

Recommended textbooks. No single text book is available which will cover all the material from the module. Useful texts are: Foundations of Engineering Acoustics by Frank Fahy. Publisher: Academic Press Ltd. Library class mark: TA365 FAH Active Control of Sound by P.A. Nelson and S.J. Elliott. Publisher: Academic Press Ltd. Library class mark: QC247 NEL Sound and Sources of Sound by A.P. Dowling and J.E. Ffowcs Williams. Publisher: Ellis Horwood Ltd. Library class mark: QC225 DOW Lecture notes on the Mathematics of Acoustics Edited by M.C.M. Wright. Publisher: Imperial College Press. Library class mark: QC 223 WRI Acoustics: an introduction to its physical principles and applications by A.D. Pierce. Publisher: McGraw-Hill, Inc. Library class mark: QC225 PIE Acoustics and Aerodynamic Sound by M. Howe. Publisher: Cambridge University Press. Library class mark: TA 365 HOW The following unpublished text is available to download without charge for academic use only: An Introduction to Acoustics by S.W. Rienstra and A. Hirschberg, Eindhoven University of Technology https://www.win.tue.nl/~sjoerdr/papers/boek.pdf

### Assessment

#### Summative

MethodPercentage contribution
Examination  (120 minutes) 100%

#### Repeat

MethodPercentage contribution
Examination  (120 minutes) 100%

#### Referral

MethodPercentage contribution
Examination  (120 minutes) 100%

#### Repeat Information

Repeat type: Internal & External