MATH Project: Fourier Analysis
In a typed essay, describe the process of Fourier analysis and how it is used in the analysis of sound. You do not need to explain or demonstrate any actual calcu- lations, but you should be able to explain in words the basics of what is done, and why. What basic principles allow Fourier analysis to work? What is the purpose of Fourier analysis? What do we gain by performing Fourier analysis? Then, using the provided applet, design several sound waves of your own and observe how changes to the shape of the wave affect the timbre of the sound. What observations can you make? What patterns do you notice? How is the sound produced affected when the wave is taller/shorter/sharper/ smoother/etc.? Your essay must include answers to all of these questions, and should be at least one full page, double-spaced, with font size no larger than 12.
If you choose to use equations or formulas in your paper, and have the ability to process math symbols (say, using LaTeX or Lyx) into a typed format, that would be preferred, but if not, any equations you feel are important to include may be hand- written if they are clear and legible. Any sources used other than your classroom notes must be cited properly in some format, including the recommended resources below. MLA, APA, AMA, etc. is irrelevant to me. Your sources should be cited on a separate "works cited" page, and should not contribute to the length of your essay.
Recommended resources: (A good project can be completed using only the resources below, but there are many other excellent resources available to any moti- vated student who looks for them).
Fourier Series Applet.
Mathematics and Music, David Wright, Chapter 10, pages 109-117 from "Fourier Theory" through the end of "Example: The Square Wave." Please only use this re- source if you have some calculus experience-the calculations in this portion of the book are more complicated thann you are expected to understand (but the descrip- tions in words of the purpose of the calculations may be helpful).
"A Hard Day's Night: Solving a Beatles Mystery with Mathematics".