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MA4L4-15 Mathematical Acoustics

Department
Warwick Mathematics Institute
Level
Undergraduate Level 4
Module leader
Ed Brambley
Credit value
15
Module duration
10 weeks
Assessment
Multiple
Study location
University of Warwick main campus, Coventry

Introductory description

N/A

Module web page

Module aims

The application of wave theory to problems involving the generation, propagation and scattering of acoustic and other waves is of considerable relevance in many practical situations. These include, for example, underwater sound propagation, aircraft noise, remote sensing, the effect of noise in built-up areas, and a variety of medical diagnostic applications. This course would aim to provide the basic theory of wave generation, propagation and scattering, and an overview of the mathematical methods and approximations used to tackle these problems, with emphasis on applications to aeroacoustics.

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

*Some general acoustic theory.
*Sound generation by turbulence and moving bodies (including the Lighthill and Ffowcs WilliamsHawkings acoustic analogies). *Scattering (including the scalar Wiener-Hopftechnique applied to the Sommerfeld problem of scattering by a sharp edge)
*Long-distance sound propagation including nonlinear and viscous effects.
*Wave-guides.

Learning outcomes

By the end of the module, students should be able to:

  • Reproduce standard models and arguments for sound generation and propagation
  • Apply mathematical techniques to model sound generation and propagation in simple systems
  • Understand and apply Wiener-Hopf factorisation in the scalar case

Indicative reading list

[1] A.D.Pierce, "Acoustics", McGraw-Hill1981.
[2] D.G.Crighton, A.P.Dowling, J.E.FfowcsWilliams, et al, "Modern Methods in Analyticial Acoustics", Springer 1992.
[3] L.D.Landau & E.M.Lifshitz, "Fluid Mechanics", Elsevier 1987.

Subject specific skills

To understand the underlying mathematical tools of acoustics sufficiently to read current research publications on acoustics. To be able to apply these techniques to current research questions within mathematics, engineering and industry. In particular, on successfully passing this module, a student would be able to understand the professional papers presented to the key academic-industrial conferences.

Transferable skills

Students will acquire key reasoning and problem solving skills which will empower them to address new problems with confidence.

Study time

Type Required
Lectures 30 sessions of 1 hour (20%)
Tutorials 9 sessions of 1 hour (6%)
Private study 111 hours (74%)
Total 150 hours

Private study description

Independent study, non-assessed example sheets and revision for exam.

Costs

No further costs have been identified for this module.

You do not need to pass all assessment components to pass the module.

Students can register for this module without taking any assessment.

Assessment group B1
Weighting Study time Eligible for self-certification
Online Examination 100% No
  • Answerbook Gold (24 page)
Assessment group R
Weighting Study time Eligible for self-certification
Online Examination 100% No
  • Answerbook Gold (24 page)
Feedback on assessment

Marked coursework and exam feedback.

Past exam papers for MA4L4

Courses

This module is Optional for:

  • TMAA-G1PE Master of Advanced Study in Mathematical Sciences
    • Year 1 of G1PE Master of Advanced Study in Mathematical Sciences
    • Year 1 of G1PE Master of Advanced Study in Mathematical Sciences
  • Year 1 of TMAA-G1P0 Postgraduate Taught Mathematics
  • Year 1 of TMAA-G1PC Postgraduate Taught Mathematics (Diploma plus MSc)
  • Year 1 of TPXA-F344 Postgraduate Taught Modelling of Heterogeneous Systems
  • Year 2 of TPXA-F345 Postgraduate Taught Modelling of Heterogeneous Systems (PGDip)

This module is Core option list D for:

  • Year 4 of UMAA-GV19 Undergraduate Mathematics and Philosophy with Specialism in Logic and Foundations

This module is Option list A for:

  • Year 1 of TMAA-G1PD Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc)
  • Year 1 of TMAA-G1P0 Postgraduate Taught Mathematics
  • Year 1 of TMAA-G1PC Postgraduate Taught Mathematics (Diploma plus MSc)
  • Year 4 of UPXA-FG33 Undergraduate Mathematics and Physics (BSc MMathPhys)
  • Year 4 of UPXA-FG31 Undergraduate Mathematics and Physics (MMathPhys)
  • Year 4 of USTA-G1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)

This module is Option list B for:

  • Year 1 of TMAA-G1PD Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc)
  • Year 1 of TMAA-G1PC Postgraduate Taught Mathematics (Diploma plus MSc)
  • Year 1 of TPXA-F345 Postgraduate Taught Modelling of Heterogeneous Systems (PGDip)
  • Year 4 of UCSA-G4G3 Undergraduate Discrete Mathematics
  • Year 3 of USTA-G1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
  • Year 4 of USTA-G1G4 Undergraduate Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)

This module is Option list C for:

  • UMAA-G105 Undergraduate Master of Mathematics (with Intercalated Year)
    • Year 3 of G105 Mathematics (MMath) with Intercalated Year
    • Year 5 of G105 Mathematics (MMath) with Intercalated Year
  • UMAA-G103 Undergraduate Mathematics (MMath)
    • Year 3 of G103 Mathematics (MMath)
    • Year 4 of G103 Mathematics (MMath)
  • UMAA-G106 Undergraduate Mathematics (MMath) with Study in Europe
    • Year 3 of G106 Mathematics (MMath) with Study in Europe
    • Year 4 of G106 Mathematics (MMath) with Study in Europe