Using interactive simulations to visualize Fourier analysis. Free

Fourier analysis is an elegant and powerful method for expressing general functions as a sum of simpler trigonometric functions. In this presentation the PhET sim “Fourier: Making Waves” http://PhET.colorado.edu/en/simulation/fourier, will be presented including the research behind the simulation, how students react to the sim, and ideas for use in class. Students typically learn the math needed to do Fourier transforms and learn how to express a function in time or space and in terms of wavelength, wave number, or mode. However, many of these relationships are only memorized for the short term (exam) and are not retained. This simulation is designed to help students visualize how a combination of simple sines and cosines can create a more complicated function and listen to the sounds produced by each harmonic. They can explore each of the symbols lambda, T, k, omega, and n to learn what each represents on the graph and their relationships with one another. There is also a game tab with ten different levels that challenges students to choose the correct harmonics to match more and more complicated functions. Finally there is a tab to help students visualize moving from a discrete to a continuous series.