MAS315 Waves

Semester 1, 2019/20 10 Credits
Lecturer: Prof Robert von Fay-Siebenburgen Home page Reading List
Aims Outcomes Teaching Methods Assessment

Studying wave phenomena has had a great impact on Applied Mathematics. This module looks at some important wave motions with a view to understanding them by developing from first principles the key mathematical tools. We begin with waves on strings (e.g., a piano or violin), developing the concept of standing and progressive waves, and normal modes. Fourier series are used to solve problems relating to waves on strings and membranes. Sound waves and water waves are considered. The concepts of dispersion and group velocity are introduced. The course concludes with consideration of "traffic waves" as the simplest example of nonlinear waves.

Prerequisites: MAS112 (Vectors and Mechanics)
No other modules have this module as a prerequisite.


Outline syllabus

  • Waves on strings. D'Alembert solution. Standing and propagating waves. Normal modes.
  • Use of Fourier series for solving one-dimensional wave problems.
  • Sound waves. Plane, cylindrical and spherical sound waves.
  • Water waves. Wave dispersion. Group velocity.
  • Traffic waves.



Aims

  • To introduce wave propagation.
  • To derive important mathematical tools to deal with problems of wave theory.
  • To consider simple examples of linear waves on strings, sound waves and water waves.
  • To give you one of simplest examples of nonlinear waves.

Learning outcomes

By the end of the unit students should have a knowledge of: 1. Waves on strings. D'Alembert solution. Standing and propagating waves. Normal modes. 2. Use of Fourier series for solving one-dimensional wave problems. 3. Sound waves. Plane, cylindrical and spherical sound waves. 4. Water waves. Wave dispersion. Group velocity. 5. Traffic waves.

Teaching methods

Lectures, problem solving


20 lectures, no tutorials

Assessment

One formal 2 hour written examination. Format: 4 questions from 5.

Reading list

Type Author(s) Title Library Blackwells Amazon
B See list at: http://www.robertus.staff.shef.ac.uk/ama349/info.html

(A = essential, B = recommended, C = background.)

Most books on reading lists should also be available from the Blackwells shop at Jessop West.