Wave Propagation and its Applications for High School Students using Mathematica

Vaishnavi Giridaran, Karolina Kalbarczyk, Nishant Nookala & Kareem Sayegh 
(Advised by Dr. Nahil Sobh)

University Laboratory High School

Abstract

We are all Seniors at Uni High in Urbana, IL with one prior year of Calculus in which we were introduced to single-variable Derivation, Integration, and basic Differentiation.  Our calculus teacher, Dr. Nahil Sobh hired us to work for him in a research project on wave propagation over the summer.  As a prerequisite to any in-depth exploration of waves and wave propagation we had to quickly learn how to evaluate Ordinary Differential Equations (ODE) and Partial Differential Equations (PDE) --something most first years would get lost in.  However, with the help of our instructor and Mathematica we were able to understand the concepts and apply them in about a week.

Our goal in this project is to create a system in Mathematica for teaching high school students with one or two years of Calculus, the concepts behind ODE and PDE as well as their application to the Wave Equation and wave propagation.  They can then use their newfound knowledge to model many waves with 2-Dimensional and 3-Dimensional Plots.

We will then extend our understanding of wave propagation to explore the modeling of defects in strings or other materials (such as variations in density or cross-sectional area), especially focusing on the trapping of waves in strings.

This project is intended to show Mathematica's usefulness as a teaching tool as well as a research tool by initially using the program as an utility for teaching concepts of multi-variable calculus and then exploring those concepts past their initial scope.