Module overview
This course introduces the properties and mechanics of waves, from the derivation and solution of wave equations, through the origins of the classical processes of refraction, dispersion and interference, to the quantum mechanical phenomenon of the uncertainty principle. It will arm students with a basic knowledge of wave behaviour and propagation, together with techniques for their quantitative analysis and application to a range of physical systems. It will further provide a fundamental base from which to examine wave aspects of electromagnetism, quantum mechanics and solid state physics in subsequent courses.
Linked modules
Pre-requisites: PHYS1011 AND PHYS1013 AND PHYS1015 AND PHYS1022
Aims and Objectives
Learning Outcomes
Knowledge and Understanding
Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:
- Express the nature of wave propagation and its physical mechanisms
- Differentiate interference and diffraction, the Huygens principle, Fraunhofer diffraction, diffraction gratings
- Depict the energy and momenta of wave motions
- Define dispersion and the phase and group velocities
Transferable and Generic Skills
Having successfully completed this module you will be able to:
- Relate superpositions, wave packets and Fourier analysis
Subject Specific Intellectual and Research Skills
Having successfully completed this module you will be able to:
- Interpret the physical basis of continuity conditions and their implications for interfaces
Subject Specific Practical Skills
Having successfully completed this module you will be able to:
- Derive the solution of wave equations, both in one and three dimensions
- Distinguish the travelling, standing and harmonic wave solutions
Syllabus
- General principles of wave propagation; derivation and solution of wave equations
- Transverse waves; travelling, standing and harmonic solutions; initial conditions
- Linearity, interference, superposition and the Huygens construction for wave propagation
- Fourier series and transforms; the convolution theorem
- Wave packets, dispersion and phase and group velocities
- Diffraction: single slit, double slit, grating and general Fraunhofer results
- Energy and momentum transport in wave motions
- Continuity conditions and interfaces
- Longitudinal waves; waves from moving sources; waves in various physical systems
- Wave mechanical operators; wavefunction averages; transform limits and uncertainty
Learning and Teaching
| Type | Hours |
|---|---|
| Follow-up work | 18 |
| Preparation for scheduled sessions | 18 |
| Lecture | 36 |
| Completion of assessment task | 10 |
| Wider reading or practice | 46 |
| Tutorial | 12 |
| Revision | 10 |
| Total study time | 150 |
Resources & Reading list
Textbooks
A. P. French (1971). Vibrations and Waves. London: various publishers: Chapman and Hall, London; W W Norton,New York; Nelson Thornes, Cheltenham.
E Hecht (2001). Optics. Addison-Wesley.
Tim Freegarde (2012). Introduction to the Physics of Waves. Cambridge: Cambridge University Press.
R P Feynman (2011). Lectures in Physics vol 1. Basic Books.
H. H. Pain (1998). The Physics of Vibrations and Waves. Chichester: Wiley.
I.G. Main (1993). Vibrations and Waves in Physics. Cambridge: Cambridge University Press.
Assessment
Assessment strategy
Course work worth 20% of the module mark will be set and assessed in the normal way. In the event that a course work is missed, students will be required to go through the Special Considerations procedures in order to request mitigation for that piece of course work. Please note that documentary evidence will normally be required before these can be considered.
The final exam is worth 80% of the module mark.
Referral Method: By examination, the final mark will be calculated both with and without the coursework assessment mark carried forward, and the higher result taken.
Summative
This is how we’ll formally assess what you have learned in this module.
| Method | Percentage contribution |
|---|---|
| Problem Sheets | 20% |
| Examination | 80% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
| Method | Percentage contribution |
|---|---|
| Examination | 80% |
| Coursework marks carried forward | 20% |
Repeat
An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.
| Method | Percentage contribution |
|---|---|
| Examination | 80% |
| Coursework marks carried forward | 20% |
Repeat Information
Repeat type: Internal & External