Engineering and the Environment, University of Southampton

Knowledge and understanding
Having successfully completed the module, you will be able to:

• Define a wave, and identify the difference between a transverse and longitudinal wave.
• Define phase and group velocity, and apply these concepts to a time-harmonic wave and a wave group.
• Explain the difference between dispersive and non-dispersive waves.
• Derive (from Newton’s 2nd Law) the equation of motion for a spring-bob oscillator.
• Outline the derivation (from conservation of mass and Newton’s 2nd Law) of the 1D acoustic wave equation.
• Identify the difference between an isothemal and adiabatic process.
• Show that the given solution of the 1D acoustic wave equation is a plane wave, and determine the direction of propagation.
• Calculate the specific acoustic impedance of a plane wave.
• Derive the relationships between particle displacement, particle velocity and acoustic pressure.
• Calculate the SPL from coherent and incoherent sources.
• Derive (by using conservation of energy) suitable expressions for cylindrical and spherical waves.
• Derive and apply Snell’s law in order to calculate refraction at a fluid-fluid interface.
• Derive pressure reflection R and transmission T coefficients at a plane boundary (at normal incidence).
• Apply R and T to a pressure-release and rigid boundary.
• Describe the formation of standing waves in an impedance tube, and recognize the effect of changing the impedance of the sample in the tube.
• Construct normal modes of free oscillation in a 1D system.
• Apply the method of images to the reflection of a spherical wave at a plane boundary.

Cognitive (thinking) skills
Having successfully completed the module, you will be able to:

• Appreciate the relevance of acoustics in practical applications.
• Analyse simple acoustics problems, and utilize mathematical modelling to solve the problem.
• Recognize examples of common wave phenomena.
• Improved ability to read and interpret scientific textbooks.

Practical, subject specific skills
Having successfully completed the module, you will be able to:

• Recognize that physical quantities which vary sinusoidally may be expressed in complex exponential form, and appreciate the benefits of this approach.
• Recognize and define terms specific to acoustics.
• Apply Huygen's principle to practical examples of wave propagation, diffraction and refraction.
• Calculate the shift in frequency caused by the Doppler effect.
• Conduct simple acoustics experiments.

Key transferable skills
Having successfully completed the module, you will be able to:

• Improved ability to carry out laboratory work.
• Write laboratory reports.
• Critically evaluate experimental data.
• Ability to read and understand scientific textbooks.
• Improved ability to utilize mathematical modeling of simple engineering problems.

The aim of this module is to introduce some of the fundamental theory of acoustics, with emphasis on the underlying physical principles.

• To introduce the student to some of the fundamental theory of acoustics.
• To describe longitudinal wave propagation.
• To derive the plane wave equation, and discuss its solutions.
• To calculate cylindrical and spherical wave spreading, reflection coefficients at a plane boundary, refraction at a plane fluid-fluid interface and normal modes of free oscillation in one dimension.
• To give the student experience of solving simple problems in acoustics.

• 1. Introduction: (approx. two lectures)
  a. Sound waves
  b. Applications of acoustics
  c. Some common wave phenomena

• 2. Physical description of the longitudinal wave: (approx. two lectures)
  a. Compression waves
  b. Acoustic plane waves
  c. Time-harmonic waves
  d. Dispersive and non-dispersive waves

• 3. Comparison of the oscillator and the wave: (approx. two lectures)
  a. Simple Harmonic Motion
  b. Plane Wave Equation
  c. Derivation of the Plane Wave Equation

• 4. Application of the Plane Wave Equation: (approx. two lectures)
  a. Solutions of the Plane Wave Equation
  b. Sound waves in gases and liquids
  c. Harmonic plane waves
  d. Acoustic impedance
  e. Summary for a harmonic plane wave

• 5. Energy and Intensity: (approx. three lectures)
  a. Energy, Power and Intensity
  b. Intensity of a plane acoustic wave
  c. Sound from multiple sources
  d. Spherical and cylindrical waves
  e. Huygens principle
  f. Snell’s law

• 6. Reflection: (approx. four lectures)
  a. Reflection of a plane wave at normal incidence
  b. Pressure-release and rigid boundaries
  c. Plane standing waves
  d. Normal modes
  e. Image sources

2 lectures per week
1 tutorial session per week
1 laboratory

Lecture notes are provided which, in general, cover the theory listed in the module syllabus. In addition to explaining the theory outlined in the notes, a set of worked examples are presented during the lectures. Students should make their own notes for these worked examples.

Students are encouraged to undertake further reading, and a booklist together with recommended reading is provided.

Problem sheets and specimen answers are provided, and solutions are discussed during regular tutorial sessions.

Also, at the end of the course there are a series of revision lectures, which include a review of past exam questions.

Students are encouraged to attempt the problem sheets and past exam papers. The problem sheets may be marked by the lecturer providing the students with formative feedback during the course (if requested).

Core text

Foundations of Engineering Acousticsbr>1st edition, 2001, F.J. Fahy, Academic Press
0 1224 7665 4

Fundamentals of Acoustics
4th edition, 2000
3rd edition, 1982
2nd edition, 1962, L.E.Kinsler
A.R. Frey
A.B. Coppens
J.V. Sanders, John Wiley
0471094102 pbk
0471029335 hbk