Module overview
This module introduces students to mathematical and numerical methods to solve practical problems in acoustics. It provides a self-contained review and derivation of the equations of linear acoustics in the time and frequency domains. Mathematical modelling of sound fields generated by complex source distributions is introduced. This leads to more advanced mathematical methods commonly used in acoustics such as the acoustic Green function and integral solutions of the acoustic wave equation. The numerical methods which are covered in the course are available as commercial software packages but the underpinning theory and analysis is discussed in sufficient technical detail to serve as a starting point for those seeking to apply or extend them to research problems.
Linked modules
Prerequisite: ISVR1032 and ISVR2042
Aims and Objectives
Learning Outcomes
Subject Specific Intellectual and Research Skills
Having successfully completed this module you will be able to:
- Validate a numerical acoustics code against a relevant benchmark acoustic problem. [EA3p]
- Formulate solutions to predict sound fields generated by complex source distributions. [SM2m]
- Recognise more advanced mathematical methods in analytical acoustics. [SM1p]
- Assess the suitability of different numerical methods for some practical acoustical problems. [SM5m]
Transferable and Generic Skills
Having successfully completed this module you will be able to:
- Synthesise information from a range of sources. [EP4i]
- Communicate clearly in written reports. [D6p]
- Read, understand, and interpret scientific texts. [EP4i]
- Apply critical analysis and evaluation skills. [SM3p]
Subject Specific Practical Skills
Having successfully completed this module you will be able to:
- Recognise that Green function theory can be used for solving partial differential equations. [SM2i]
- Determine the mesh requirements and boundary conditions for simulating target acoustic problems. [EA3p]
- Apply the numerical methods presented in the course to problems in acoustics. [EA3p]
- Understand user documentation for commercial acoustic codes and use relevant tools to create simple computational models, perform analysis and post-process results. [SM5m]
Knowledge and Understanding
Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:
- Trade-off between computational cost and accuracy. [SM5m]
- Boundary conditions for practical acoustic problems. [SM5m]
- Integral solutions of the inhomogeneous Helmholtz equation using the acoustic Green function. [SM2p]
- Advanced mathematical methods associated with modelling sound fields generated by complex source distributions. [SM5m]
- Some background theories, features and limitations of Finite Element and Boundary Element Methods in the frequency domain for acoustics. [SM5m]
- The equations that govern the propagation of sound in a stationary medium. [SMm5]
Syllabus
Indicative content:
- Revision of fluid dynamics
- Derivation of equations for linear acoustics. Wave equation
- Time-harmonic acoustics. Complex notation and the Helmholtz equation
- Finite Element Method for the Helmholtz problem: 1-D elements
- Numerical dispersion and dissipation, the pollution effect.
- Finite Element Method for the Helmholtz problem: 2D and 3D elements.
- Acoustic sources. Inhomogeneous wave and Helmholtz equations
- The acoustic Green function
- Integral solutions of the inhomogeneous Helmholtz equation
- Boundary Element Method for the Helmholtz problems in 2D and 3D fields.
- A range of benchmark examples/applications in physical acoustics
Learning and Teaching
Teaching and learning methods
The course will be delivered by using a mixture of interactive lecture/tutorial sessions. These sessions will be used to present the theory and worked examples. Lecture notes will be available in electronic format on Blackboard.
Problems sheets will be provided which contain exercises similar to the worked examples presented during the lectures. Solutions to the exercises will be provided on Blackboard.
Solutions to problems will be covered at tutorial sessions.
Revision lectures will be given at the end of the course to prepare students for the exam.
A summative coursework assignment will require the students to solve acoustics problems by writing simple programmes or by using commercial acoustics software.
| Type | Hours |
|---|---|
| Tutorial | 6 |
| Revision | 24 |
| Follow-up work | 24 |
| Wider reading or practice | 12 |
| Preparation for scheduled sessions | 24 |
| Completion of assessment task | 30 |
| Lecture | 30 |
| Total study time | 150 |
Resources & Reading list
General Resources
Software requirement. Access to classkit Licence for COMSOL (acoustics module).
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
| Method | Percentage contribution |
|---|---|
| Continuous Assessment | 50% |
| Final Assessment | 50% |
Repeat Information
Repeat type: Internal & External