MPhys Physics with Theoretical Physics / Course details

Vibrations & Waves

• Mathematics 1 PHYS10071 OR Introduction to Vector Calculus MATH11411
• Dynamics PHYS10101

To explore the detailed behaviour of vibrating systems and wave motion in many different physical systems.

On completion successful students will be able to:

1. describe and quantitively analyse the behaviour of oscillating systems and wave motion.
2.  apply the mathematical formalism that describes them.
3. identify examples of oscillating systems and wave motion across many areas of physics

Vibrations & Waves

Simple harmonic motion (SHM) (10 lectures) 

1. Simple harmonic motion. 
2. Damped SHM, energy in a vibrating system and quality factor. 
3. Forced SHM and transient response, resonance and power resonance curves. 
4. Coupled oscillators, normal modes, vibrations of the CO2 molecule. 

Waves (8 lectures) 

1. The 1-D wave equation. 
2. Waves at interfaces. 
3. Wave energy and power. 
4. Standing Waves. The wave equation in 2-D and 3-D. Wave superposition. 
5. Phase and group velocity. Beats. Dispersion.

Applications (4 lectures) 

1. Interference and diffraction.Bragg’s law. 
2. 1D chains of atoms with equal and unequal masses using matrix notation, normal modes. 

Examples of vibrating systems and waves will be given in the lectures and on the problem sheets.

Assessment - Exam

Tutorial

Lecture

Independent Study

* 10% Tutorial Work/attendance 

Feedback will be offered by tutors on students’ written solutions to weekly examples sheets, and model answers will be issued.

Printed summaries will be downloadable. 

King G.C., Vibrations and Waves (Manchester Physics Series, Wiley, 2009)