# Notes on Wave Equation 2D 1.0b 9/5/95

Wave Equation 2D is a Macintosh program which solves the two dimensional wave equation in a square region. The solutions of this equation may be interpreted as the vibrations of a square drum head, small amplitude waves in a square swimming pool, or as idealised sound or electromagnetic waves in a square planar cavity. The program does not assume any knowledge of any of these subjects on the part of the user, and does not require any programming of any kind. It does assume that you have the concept of an initial condition, which is the idea that the state of things evolves from some starting state, which in this case consists of a wave shape and a wave velocity, since the wave equation is second order in time. You can run the program without understanding the Mathematics, and probably learn something and be entertained, but normally one would have studied ODEs for a while before jumping into equations like this one. On the other hand, you do not need to have studied the Wave Equation prior to using this program; in fact the main purpose of the program is to give the user some idea of what to expect, visually, from solutions before embarking on a formal study of the Mathematics.

The program allows changes in the initial and boundary conditions, and even allows the placement of barriers (or "break-waters") within the square, so that you can design your own "harbors", so to speak. The wave can be viewed either in perspective or in a plan view using color to represent height. The presentation is entirely visual.

Wave Equation 2D requires a Macintosh computer running System 7 and it would be better to have at least the standard 14" monitor- I have not tried it on laptops. The program has been tested at least on Quadra 610 and 950, Centris 650, and Power Mac 7100.

Wave Equation 2D is the latest in a sequence of educational PDE solvers that I have written, in an attempt to provide a user-friendly introduction to these equations. The previous programs are called Heat Equation 1D, Heat Equation 2D, and Wave Equation. All four programs are available in the Mathematics Archives at archives.math.utk.edu or from the author.

Robert E. (Bob) Terrell Mathematics Department, Cornell U. Ithaca, NY 14853 bterrell@math.cornell.edu Last Update: September 19, 1995