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# MA4L4 Mathematical Acoustics

Lecturer: Ed Brambley

Term(s): Term 1

Status for Mathematics students: List C

Commitment: 30 one hour lectures

Assessment: 100% Exam (3 hours)

Prerequisites: MA244 Analysis III (for contour integration); MA250 Introduction to PDEs (for Greenâ€™s
functions). MA3D1 Fluid Dynamics is useful but not necessary.

Content:

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

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 aims 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.

Objectives:
By the end of the module the student 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

Books:

• A.D. Pierce, "Acoustics", McGraw-Hill 1981
• D.G. Crighton, A.P. Dowling, J.E. Ffowcs Williams, et al, "Modern Methods in Analyticial Acoustics", Springer 1992
• L.D. Landau & E.M. Lifshitz, "Fluid Mechanics", Elsevier 1987

## Additional Resources

Archived Pages: 2017 2018