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)

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

SEE IT IN THE LECTURE
Bell Labs Wave Machine and Bell Labs Wave Machine
Rijke Tube

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

* 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

Fall 2016
##### Learning Resource Types
Lecture Videos
Lecture Notes
Problem Sets
Instructor Insights
Exams