8.03SC | Fall 2016 | Undergraduate
Physics III: Vibrations and Waves
Part I: Mechanical Vibrations and Waves

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.

Lecture Notes

Typed Notes for Lecture 9 (PDF - 1.1MB)

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 and Bell Labs Wave Machine
Rijke Tube

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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Course Info
As Taught In
Fall 2016
Learning Resource Types
theaters Lecture Videos
notes Lecture Notes
assignment Problem Sets
grading Exams with Solutions
co_present Instructor Insights