Finding Particular Solutions via Fourier Series; Resonant Terms; Hearing Musical Sounds

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Taught by OCW

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Lesson Description:

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

Additional Resources:

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

Questions answered by this video:

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
- Currently 4.0/5 Stars.
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.

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