Description

The module first considers 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 (key to much of solid-state physics) are also discussed, followed by an introduction to geometrical optics and optical systems.

Module Aims

The concepts of oscillation amd wave propagation permeate the whole of physics. This module identifies and applies the underlying principles enabling the student to understand many apparently unrelated systems. A wide range of physical phenomena are used as examples. The concepts introduced in this module underpin, and will be developed in later modules, e.g. in PHY2021 Electromagnetism I, PHY2022 Quantum Mechanics I and PHY2024 Condensed Matter I.

Intended Learning Outcomes (ILOs)

A student who has passed this module should be able to:

• Module Specific Skills and Knowledge:
  1. set up the equations associated with simple-harmonic motion, solve them for different physical conditions and recognise situations where they are applicable;
  2. 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;
  3. 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;
  4. solve problems involving simple systems of lenses and mirror, derive relations such as the lens makers formula, describe the origin and use of total internal reflection;
  5. describe Young's experiment using complex amplitudes and phasors;
  6. calculate the diffraction limited resolution of a simple imaging system;
  7. discuss thin-film interference fringes and anti-reflection coatings and calculate the properties needed by an optimal anti-reflection coating.
  8. describe the diffraction grating, Fabry-Perot, and Michelson interferometers and their use as spectrometers, and calculate their dispersion and resolving power;
  9. discuss the origin of polarisation, its generation and manipulation via dichroism and birefringence;
  10. describe important features of laser light such as coherence, monochromaticity and directionality;
• Discipline Specific Skills and Knowledge:
  11. make a Fourier-series expansion of a simple periodic function;
  12. to take notes in lectures and then refine them later thereby developing skills in the efficient summarising of material;
• Personal and Key Transferable / Employment Skills and Knowledge:
  13. undertake guided self-study successfully;
  14. develop appropriate time-management strategies and meet deadlines for completion of work.

Syllabus Plan

1. Introduction
   Brief historical survey.
2. The Physics of Simple and Damped Harmonic Motion (SHM)
   1. SHM - mass on a spring, equation of motion
   2. Phase angle, displacement, velocity, acceleration
   3. Energy of simple harmonic motion
   4. Damped SHM (mechanical system) - oscillatory and logarithmic decrement (exponential notation)
   5. Quality factor, Q - energy dissipation
   6. Critical-, under- and over-damped mechanical systems
3. Forced Oscillator
   1. Steady-state solution for mass on a spring plus driving force
   2. Mechanical impedance (complex impedance, amplitude, phase factor); amplitude resonance; power supplied by the driving force, Q-value
4. 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; power in AC circuits; series and parallel resonance
5. Introduction to Waves
   1. The electromagnetic spectrum
   2. Definition and examples of wave motion; transverse and longitudinal waves; polarization; plane and spherical waves
   3. Basic wave concepts: amplitude and phase; wave number k and angular frequency ω; phase velocity
   4. The wave equation and its solutions
   5. The Doppler effect
   6. Example: transverse waves on a string
   7. Energy transfer in wave motion
6. Superposition of Waves
   1. Standing waves and normal modes
   2. Partial standing waves
   3. Fourier series
   4. Wave packets, dispersion and group velocity
   5. Example: dispersed wave on a string
7. 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
8. 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
9. Other Examples of Waves
   1. Longitudinal waves in a solid
   2. Sound waves in a gas
10. Optics
    1. Geometrical optics
       Imaging and ray tracing; thin-lenses; total internal reflection
    2. Interference and diffraction
       Young's experiment; diffraction limited resolution; diffraction-grating spectrometer; thin films and anti-reflection coatings; Fabry-Perot interferometer; Michelson interferometer
    3. Dispersion by prisms and diffraction gratings
    4. Polarization
       Electromagnetic interpretation; Generation by polarizers, reflection and scattering; Birefringence
    5. Optical cavities and laser action

Learning and Teaching

Learning Activities and Teaching Methods

Assessment

Resources

The following list is offered as an indication of the type & level of information that students are expected to consult. Further guidance will be provided by the Module Instructor(s).

Core text:

• Young H.D. and Freedman R.A. (2015), University Physics with Modern Physics (14^th edition), Pearson, ISBN 978-1-292-10031-9

Supplementary texts:

• Feynman R.P., Leighton R.B. and Sands M. (1963), Lectures on Physics, Vol. I, Addison-Wesley, ISBN 0-201-02116-1
• Hecht E. (2017), Optics (5^th edition), Addison-Wesley, ISBN 978-0133977226
• Pain H.J. (2005), The Physics of Vibrations and Waves (6^th edition), Wiley, ISBN 0-470-01296-X
• Pedrotti F.L. and Pedrotti F.J.L.S. (2007), Introduction to Optics (3^rd edition), Pearson Prentice-Hall, ISBN 978-0-131-97133-2

ELE:

• http://newton.ex.ac.uk/redirects/ELE/phy1023

Further Information

Prior Knowledge Requirements

Re-assessment

Re-assessment is not available except when required by referral or deferral.

Notes: See Physics Assessment Conventions.

KIS Data Summary

Miscellaneous