Lecture 9: Wave Equation, Standing Waves, Fourier Series

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Lecture Topics

  • Standing waves
  • Vibrating string
  • Wave equation
  • Fourier series
  • Fourier decomposition

Lecture Video: Wave Equation, Standing Waves, Fourier Series

The standing wave solution of the wave equation is the focus this lecture. Using a vibrating string as an example, Prof. Lee demonstrates that a shape can be decomposed into many normal modes which could be used to describe the motion of the string.

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Lecture Notes

This resource may not render correctly in a screen reader.Typed Notes for Lecture 9 (PDF - 1.1MB)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 9 (PDF - 1.7MB)

Textbook Reading

Chapter 5: Waves (PDF - 1.4MB) (section 5.3 to end)

Chapter 6: Continuum Limit and Fourier Series (PDF - 1.2MB) (through section 6.1)

Problem Set

Problem Set 5 (PDF)

Problem Solving Help Video*

Traveling Waves without Damping

Standing Waves Part I

Standing Waves Part II

In-class Demonstrations

Bell Labs Wave Machine @ 00:24:18 and @ 00:48:57
Rijke Tube @ 00:26:22

Related Resources

Video: Air Conditioner Noise by Prof. Yen-Jie Lee

Video: Intro to Fourier Series and How to Calculate Them by Dr. Chris Tisdell

Webpage: Fourier Series: Basics on OCW’s 18.03SC Differential Equations course







* Note: These Problem Solving Help video was originally produced as part of a physics course that is no longer available on OCW.

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