Sound as an Additional Learning Tool

One of the advantages of using Mathematica in basic math courses is that it opens up the possibility of creating experiments in mathematics. In electrical engineering courses at Chalmers University College, we have used sound as an experimental tool to investigate aspects of mathematics that otherwise tend to elude students. We give examples from two areas: ordinary differential equations and Fourier analysis. In the first example, we let Mathematica solve a differential equation with a parameter and then play the sound of the solution for different values of that parameter. The object is to find beat and resonance by listening. In the second example, we expand different functions in the Fourier series and then listen to the functions and partial sums of these series.