Introduction

Oscillations and waves are ubiquitous phenomena that are observed in a wide range of different physical systems. An oscillation is a disturbance in a physical system that is repetitive in time. A wave is a disturbance in an extended physical system that is both repetitive in time and periodic in space. In general, an oscillation involves a continual back and forth flow of energy between two different energy types: e.g., kinetic and potential energy, in the case of a pendulum. A wave involves similar repetitive energy flows to an oscillation, but, in addition, is capable of transmitting energy (and information) from place to place. Now, although sound waves and electromagnetic waves, for example, rely on quite distinct physical mechanisms, they, nevertheless, share many common properties. This is also true of different types of oscillation. It turns out that the common factor linking the various types of wave is that they are all described by the same mathematical equations. Again, this is also true of the various types of oscillation.

The aim of this course is to develop a unified mathematical theory of oscillations and waves in physical systems. Examples will be drawn from the dynamics of discrete mechanical systems; continuous gases, fluids, and elastic solids; electronic circuits; electromagnetic waves; and quantum mechanical systems.

This course assumes a basic familiarity with the laws of physics, such as might be obtained from a two-semester introductory college-level survey course. Students are also assumed to be familiar with standard mathematics, up to and including trigonometry, linear algebra, differential calculus, integral calculus, ordinary differential equations, partial differential equations, and Fourier series.

The textbooks which were consulted most often during the development of the course material are:

Waves, Berkeley Physics Course, Vol. 3, F.S. Crawford, Jr. (McGraw-Hill, New York NY, 1968).

Vibrations and Waves, A.P. French (W.W. Norton & Co., New York NY, 1971).

Introduction to Wave Phenomena, A. Hirose, and K.E. Lonngren (John Wiley & Sons, New York NY, 1985).

The Physics of Vibrations and Waves, 5th Edition, H.J. Pain (John Wiley & Sons, Chichester UK, 1999).