## PHYS1051 Vibrations and Waves

### 10 creditsClass Size: 150

Module manager: Dr S H Kilcoyne
Email: s.h.kilcoyne@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2005/06

### Pre-requisite qualifications

A-Level Physics and Mathematics or equivalent

This module is approved as an Elective

### Module summary

Vibrations and waves are ubiquitous phenomena in the world. In spite of occurring in widely different physical systems, they can be described by a common mathematical approach.In the course, we study simple and damped harmonic motion, the characteristics of waves, such as their superposition, interference and diffraction in light and sound, and geometrical optics, namely refraction, reflection, lenses and optical instruments.

### Objectives

At the end of this module you should be able to:

- describe harmonic vibrations using mathematical formulae;
- calculate the properties of vibrating systems;
- describe the properties of waves and predict their motion;
- derive and utilise the wave equation;
- derive and utilise the laws of reflection and refraction;
- perform simple calculations on basic optical instruments;
- describe and differentiate between diffraction and interference of light.

Skills outcomes
Ability to model a physical problem.
Ability to solve mathematical problems.Ability to model a physical problem.
Ability to solve mathematical problems.

### Syllabus

Vibrations: Simple harmonic motion, damped oscillations, driven oscillations and resonance.

Waves: Characteristics of waves, wave pulses, harmonic waves, the wave equation, energy transport, superposition and interference of waves, standing waves, the wave equation

Sound: Sound waves, hearing, interference of sound waves, beats. The Doppler effect.

Geometrical Optics: Refraction, reflection, Snell's law, total internal reflection, simple image formation by lenses, the eye, basic optical instruments.

Interference of light waves: Interference pattern of a double slit, the diffraction grating.

Diffraction of light waves: Diffraction pattern of a single slit, limit of resolution of an optical system.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Lectures: 22 x 1 hour;

Tutorials: 3 x 1 hour;

Problem-solving classes: 3 x 1 hour.

### Private study

Preparing tutorials and problems: 12 hours;
Revision: 38 hours.

### Opportunities for Formative Feedback

3 assignments and 3 tutorials.

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

1 x 2 hour written examination: 85%;
Marked work from problem-solving classes: 15%.