Finding Particular Solutions via Fourier Series; Resonant Terms; Hearing Musical Sounds
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.
More info at: http://ocw.mit.edu/terms
- Lecture Notes - Lecture Notes
- Notes - Notes and exercises written by Prof. Mattuck
- Supplementary Notes - Chapter 12 Supplementary Notes written by Prof. Miller
- Problem Set 4 - Problem Set 4
- Problem Set 4 Solutions - Problem Set 4 Solutions
- Recitation Problems - Recitation Problems and classwork exercises
- Recitation Solutions - Recitation problem solutions
- What is the mathematical basis for hearing?
- How does math explain hearing?
- What are Fourier series?
- What are resonant terms?
- How do you find a particular solution to a Fourier series?
-
Staff Review
This is a really interesting application of resonance and vibrations. You will learn how Fourier series and the vibration of air waves explains how we can hear musical notes. You will also learn how to find particular solutions using Fourier analysis. A really important and interesting lecture in differential equations.
-%20direction%20fields,%20integral%20curves.jpg)
%20and%20its%20generalizations.jpg)
.jpg)
