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) or ISVR6136
Aims and Objectives
Learning Outcomes
Transferable and Generic Skills
Having successfully completed this module you will be able to:
- Read, understand, and interpret scientific texts and papers.
- Apply critical analysis and evaluation skills.
- Synthesise information from a range of sources.
- Communicate clearly in written reports.
Knowledge and Understanding
Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:
- Integral solutions of the inhomogeneous Helmholtz equation using the acoustic Green function.
- The equations that govern the propagation of sound in a stationary medium.
- Advanced mathematical methods associated with modelling sound fields generated by complex source distributions.
- Computational requirements of numerical analyses and trade-off between cost and accuracy.
- The background theories, features and limitations of Finite Element and Boundary Element Methods in the frequency domain for acoustics.
- Boundary conditions for practical acoustic problems.
Subject Specific Practical Skills
Having successfully completed this module you will be able to:
- Determine the mesh requirements and boundary conditions for simulating target acoustic problems.
- Understand user documentation for commercial acoustic codes and use relevant tools to create computational models, perform analysis and post-process results.
- Reduce real world acoustical problems to more simple problems amenable to numerical solution.
- Apply Green function theory for solving partial differential equations.
- Apply the numerical methods presented in the course to problems in acoustics and other areas.
Subject Specific Intellectual and Research Skills
Having successfully completed this module you will be able to:
- Assess the suitability of different numerical methods for a wide range of practical acoustical problems.
- Formulate solutions to predict sound fields generated by complex source distributions.
- Use more advanced mathematical methods in analytical acoustics.
- Write simple Finite and Boundary Element codes for the Helmholtz problem.
- Validate numerical acoustics codes against a relevant benchmark acoustic problem.
Full CEng Programme Level Learning Outcomes
Having successfully completed this module you will be able to:
- The module contains analytical and numerical methods used in acoustical engineering, and an understanding of the limitations of the methods (and error analysis for the numerical methods). The methods are applied to model complex problems in acoustics involving generation and radiation of sound in both interior and exterior domains. The use of both analytical and numerical methods for complex problems in acoustical engineering is assessed by coursework and examination.
- The module includes the use of first principles in mathematics to solve complex problems. The module also includes engineering judgement for mesh design and an understanding of errors associated with the finite and boundary element numerical methods. Solutions involving first principles in mathematics applied to acoustical engineering problems are assessed by examination. Applying numerical methods to practical problems in acoustics and recognising the limitations of the techniques is assessed by coursework.
- The module contains advanced topics on analytical methods and numerical methods in the field of acoustical engineering. The analytical methods include the mathematical formulation of complex problems involving acoustic sources radiating into interior and exterior domains. The numerical methods include the mathematical formulations that underpin the finite and boundary element methods which are widely used in engineering. The solution of complex problems in acoustical engineering is assessed by coursework and examination.
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.
- Introduction to advanced techniques and other methods
- 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.
For advanced topics, additional material for self-study will be provided to supplement the lectures.
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. Additional tutorials will be provided for students studying the level 7 version of this module. At these tutorials, solutions to more advanced problems will be covered.
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 | 12 |
Lecture | 24 |
Wider reading or practice | 12 |
Completion of assessment task | 30 |
Preparation for scheduled sessions | 24 |
Revision | 24 |
Follow-up work | 24 |
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 |
---|---|
Exam | 50% |
Assignment | 50% |
Repeat Information
Repeat type: Internal & External