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MA961-15 Mathematical Acoustics

Department
Warwick Mathematics Institute
Level
Taught Postgraduate Level
Module leader
Ed Brambley
Credit value
15
Assessment
100% exam
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.

Additional reading material might be set. This will be arranged in conjunction between the module leader and the student's mentors/supervisors and based on the research interests of the student.

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 (77%)
Tutorials 9 sessions of 1 hour (23%)
Total 39 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.

Assessment group B
Weighting Study time Eligible for self-certification
Assessment component
Viva voce examination 100% Yes (extension)

PhD Viva

Reassessment component is the same
Feedback on assessment

Marked coursework and oral exam feedback.

Past exam papers for MA961

Courses

This module is Optional for:

  • Year 1 of RMAA-G1P1 Postgraduate Research Interdisciplinary Maths
  • RMAA-G1P4 Postgraduate Research Mathematics
    • Year 1 of G1P4 Mathematics (Research)
    • Year 1 of G1P4 Mathematics (Research)
    • Year 1 of G1P4 Mathematics (Research)
    • Year 1 of G1P4 Mathematics (Research)
    • Year 1 of G1P4M Mathematics (Research)
    • Year 1 of G1PH Mathematics (Research) (Co-tutelle with The University of Paris Diderot-Paris 7)
    • Year 1 of G1PMC Mathematics (Research) (co-tutelle with CY Cergy Paris University, France)
    • Year 1 of G1PMC Mathematics (Research) (co-tutelle with CY Cergy Paris University, France)
    • Year 1 of G1PNC Mathematics (University of Warwick and Eastern Institute of Technology, Ningbo)
    • Year 1 of G1PL Mathematics (co-tutelle with Universidad del País Vasco/ Euskal Herriko Unibertsitatea)
  • RMAA-G1PG Postgraduate Research Mathematics of Systems
    • Year 1 of G1PG Mathematics of Systems
    • Year 1 of G1PG Mathematics of Systems
    • Year 1 of G1PK Mathematics of Systems (co-tutelle with Sorbonne Université’)
  • RSTA-G4P0 Postgraduate Research Statistics
    • Year 1 of G4P4C Statistics (Resarch) (SUSTech Collaborative Mobility Programme)
    • Year 1 of G4P3C Statistics (Resarch) (co-tutelle with Ca'Foscari University of Venice)
    • Year 1 of G4P0 Statistics (Research)
    • Year 1 of G4P0 Statistics (Research)
    • Year 1 of G4P0 Statistics (Research)
    • Year 1 of G4P0 Statistics (Research)
    • Year 1 of G4P0 Statistics (Research)
    • Year 1 of G4P0 Statistics (Research)
    • Year 1 of G4P0 Statistics (Research)