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

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Taught by OCW
  • Currently 4.0/5 Stars.
4084 views | 1 rating
Lesson Summary:

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.

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:
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.