Sound and Harmonic Series

by Marcos Marrero Disla

Submitted : Fall 2012

Simple harmonic motions form the basis for our understanding of mechanical waves. In this project we are going to study periodic motions which are repeating motions of an object that continues to return to a given position after a fixed time interval. Sound waves, seismic waves, waves on stretched strings as well as water waves are all produced by some source of oscillation (Serway). We will focus our attention in guitar sound waves which are an example of simple harmonic motion. We are going to accomplish this by using calculus to get clear look of sound waves characteristics using harmonic series; although harmonic series diverge, by using trigonometric identities, trigonometric polynomials as well as the use of Fourier series we can observe the behavior of the waves thus figuring out the coefficients of them.

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