The module will treat the following subjects: mechanical vibrations and waves, simple harmonic oscillators & simple harmonic motion, superposition, forced vibrations and resonance, coupled oscillations and normal modes, vibrations of continuous systems, reflection and refraction, phase and group velocity. 

A selection from the following is also possible: (1) Water waves: incompressible & compressible wave equation; interfacial waves; Scholte waves, and Rayleigh waves; Acoustic-Gravity waves. (2) Optics: wave solutions to Maxwell's equations, polarization, Snell's law, interference, Huygens's principle, Fraunhofer diffraction, and gratings.

Prerequisite Module: MA1300 Mechanics I

• Set up proper equations of motion and boundary conditions for applied problems.
• Apply separation of variables, and superposition to solve the wave equation in various domains.

26 fifty-minute lectures

Some handouts will be provided in hard copy or via Learning Central, but students will be expected to take notes of lectures.

Students are also expected to undertake at least 50 hours private study including preparation of solutions to given exercises.

Skills:
Appreciate the principles of mechanics of vibrations and waves in 2 and 3 dimensions.
Use methods of separation of variables to solve problems in incompressible, compressible and elastic domains.

Transferable Skills:
Recognise, formulate and solve real-world problems in various domains.

Formative assessment is carried out by means of regular tutorial exercises.  Feedback to students on their solutions and their progress towards learning outcomes is provided during lectures.  

The summative assessment is a class test that will take place approximately half way through the module, and the written examination at the end of the module.  This gives students the opportunity to demonstrate their overall achievement of learning outcomes.  It also allows them to give evidence of the higher levels of knowledge and understanding required for above average marks.

The examination paper has two sections of equal weight.  Section A contains a number of compulsory questions of variable length but normally short.  Section B has a choice of two from three equally weighted questions.

Mechanical Vibrations and Waves

• Simple harmonic motion

• Superposition
• Forced vibrations and resonance
• Coupled oscillations and normal modes
• Waves in continuous media
• Phase and group velocity

Acoustic-gravity waves

• Wave solutions in compressible ocean

• Waves in elastic medium

• Nonlinear interaction of acoustic-gravity waves

Electromagnetic Waves

• Wave solutions to Maxwell’s equations in vacuum

• Plane waves and polarization

• Sources of EM waves: radiation, antennas

• Wave solutions to Maxwell’s equations in conductors

• Boundary conditions: transmission lines, wave guides, cavities

French, A. P. 1971. Vibrations and Waves. Norton.

Bekefi, G., and A. H. Barrett. 1977. Electromagnetic Vibrations, Waves, and Radiation. MIT Press.