Computer Simulation of the 2D Wave Equation

This project was completed by Tony, Ethan, and Thaddeus.

Hello everyone, I hope you will enjoy our web page about the 2D wave equation :) First, we will give a brief explanation regarding the math behind it. Then, a overview of how it was programed will follow. Lastly, I description of how waves effect our lives.

The math of the 2D wave equation

I'd like to start by saying that I wouldn't bore you with too many details; that would be pointless. Instead, I will breifly explain how to equation works.

With that out of the way, here's how the equation works: Basically, we start off with a flat plane. Then we begin to shake one end of the plane. The shaking causes a wave to travel across the plane. When the wave reaches the other end of the plane, it bounces off of it. To simulate movement we calculate many, many frames, and play them back at a rapid rate. Each frame's appearence is based on the previous one.

The programing of the 2D wave equation

The programing of the 2D wave equation was actually quite simple. First of all, we wrote the code it Fortran77. We used two 100 X 100 arrays to store our data, as well as several other variables. The main part of the program computed what the next frame would look like, and dumped the data to a file. AVS was used to interpet the data. Just for fun, AVS was used to add sand and an animated shark to the equation.

How waves effect our everyday lives

Waves are literally everywhere! They gives of sound and music. They effect the way we cook, move, and even think. They run through gases, liquids, and even solids. Simply put, waves are a part of virtually everything.

An equation to calculate how a 2D Wave move is important because we want to how where they will go, how fast they will go, and how they will behave, so may use them efftively. With out this equation, the microwave, for one, probably wouldn't have been invented. With out the equation, radio stations probably wouldn't be very effective. With out this equation, it would be very hard to predict the weather. In short, without the 2D wave equation, our world wouldn't be as interesting as it is today.