# 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*