PHY1106 Waves and Oscillators

2007-2008

Code: PHY1106
Title: Waves and Oscillators
Instructors: Dr P. Vukusic
CATS credits: 10
ECTS credits: 5
Availability: unrestricted
Level: 1
Pre-requisites: N/A
Co-requisites: N/A
Background Assumed: AS level Physics or equivalent
Duration: Semester II
Directed Study Time: 22 lectures
Private Study Time: 66 hours
Assessment Tasks Time: 12 hours
Observation report: 2000/01 PV (AU)

Aims

The concept of wave propagation permeates the whole of physics with many examples arising from many different physical phenomena; complete books have been written about acoustic waves, electromagnetic waves and de Broglie waves. Even so, there are common underlying principles which make it possible to understand many apparently unrelated systems. The primary aim of the module is to identify and make use of these concepts at an elementary level and also to introduce a wide range of physical phenomena as examples. The module starts by considering the characteristic parameters of a forced, damped harmonic oscillator, and relates them to the characteristic parameters of wave propagation. Later stages discuss the propagation and reflection of waves, using waves on a stretched string as the model system. Longitudinal waves in solids, sound waves in gases, and waves in periodic structures are also discussed, the last of these being the key to much of solid-state physics. The concepts introduced in this module will be developed later in the programme, e.g. in electromagnetism (PHY3143), quantum mechanics (PHY2002) and solid-state physics (PHY2009).

Intended Learning Outcomes

Students will be able to:

• set up the equations associated with simple-harmonic motion, solve them for different physical conditions and recognise situations where they are applicable;
• construct the relevant expressions for alternating current and voltage (using complex-number representation) in an electrical circuit and derive basic quantities, e.g. power dissipation;
• manipulate the wave equation and its solution, explain the concepts of wave number, phase velocity, group velocity and dispersion; apply these concepts to waves in periodic structures and to longitudinal waves in solids and gases.

Transferable Skills

Students will be expected to take notes in lectures and then refine them later giving them skills efficient summarising of material. They will be expected to manage their time so that they completed weekly homework assignments.

Learning and Teaching Methods

Lectures, worksheet assignments, tutorials and problems classes; on-line teaching resources for AU's sections, and PV's sections. Additional problems will be given during lectures (and discussed in subsequent lectures) for homework.

Assignments

Preparation for problems classes. Ten homework problem sheets.

Assessment

Problems-class assignments (10%), two mid-semester tests (40%) and one 90-minute examination (50%).

Syllabus Plan and Content

1. The Physics of Simple and Damped Harmonic Motion
   1. Simple harmonic motion - mass on a spring, equation of motion
   2. Phase angle, displacement, velocity, acceleration
   3. Energy of simple harmonic motion
   4. Damped simple harmonic motion (mechanical system) - oscillatory and logarithmic decrement (exponential notation)
   5. Quality factor Q- energy dissipation
   6. Critical and overdamped mechanical system
2. Forced Oscillator
   1. Steady-state solution for mass on a spring plus driving force
   2. Mechanical impedance (complex impedance, amplitude, phase factor)
   3. Amplitude resonance
   4. Power supplied by the driving force, Q-value
3. Alternating Electrical Currents (Steady State)
   1. Alternating voltage, phasor diagram, amplitude, phase, period
   2. Resistance, inductance and capacitance in an AC circuit: current-voltage relationships
   3. Complex impedance in AC circuits
   4. Power in AC circuits
   5. Series and parallel resonance
4. Introduction to Waves
   1. Definition and examples of wave motion. Transverse and longitudinal waves. Polarization. Plane and spherical waves
   2. Basic wave concepts: Amplitude and phase; Wave number k and angular frequency ω Phase velocity.
   3. The wave equation and its solutions.
   4. The Doppler Effect.
   5. Example: transverse waves on a string.
   6. Energy transfer in wave motion.
5. Superposition of Waves
   1. Standing waves and normal modes.
   2. Partial standing waves.
   3. Wave packets, dispersion and group velocity.
   4. Example: dispersed wave on a string.
6. Reflection and Transmission of Waves
   1. Characteristic impedance. Reflection and transmission coefficients of amplitude and energy.
   2. Example: Reflection and transmission of transverse waves on a string.
   3. Impedance matching and the quarter-wave transformer.
7. Waves on Periodic Structures
   1. Transverse waves on a one-dimensional periodic structure: dispersion relation, low-pass characteristic, first Brillouin zone.
   2. Normal modes on a one-dimensional periodic structure.
8. Other Examples of Waves
   1. Longitudinal waves in a solid.
   2. Sound waves in a gas.

Core Text

Young H.D. and Freedman R.A. (2000), University Physics (with Modern Physics) (10^th edition), Addison-Wesley, ISBN 0-201-60336-5 (UL: 530 YOU)

Supplementary Text(s)

Pain H.J. (2005), The Physics of Vibrations and Waves (6^th edition), Wiley, ISBN 0-470-01296-X (UL: 531.32 PAI)

Formative Mechanisms

Students can monitor progress through their homework marks, mid-semester tests and tutorial work.

Evaluation Mechanisms

The module will be evaluated using information gathered via the student representation mechanisms, the staff peer appraisal scheme, and measures of student attainment based on summative assessment.