In this lecture, the mathematical basis for hearing is explained. A musical tone consists of a pure oscillation, but when multiple tones are played simultaneously, the waveform becomes a mess. Fourier analysis can be used to break down the waveform into pure oscillations, allowing us to hear the individual tones that make up the sound. The lecture also covers how to find a particular solution using Fourier series and how to apply it to a general function. The superposition principle is used to find the particular solution to a sum of inputs.
Finding Particular Solutions via Fourier Series; Resonant Terms; Hearing Musical Sounds -- Lecture 17. Learn how hearing can be explained using math.
Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 27, 2008). License: Creative Commons BY-NC-SA.
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