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Physics III: Vibrations and Waves
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This resource index gives users access to most of the course resources in a single location.

Instructor Insights

INSTRUCTOR INSIGHTS VIDEOS


* Students’ Common Misconceptions
* Making Time for Individual Questions in a Large Lecture
* Using Humor to Enhance Learning
* Using Demonstrations in Class
* Behind-the-Scenes Demo Prep
* Taking a Vote to Engage Learners

Part I: Mechanical Vibrations and Waves

TITLE LECTURE VIDEOS LECTURE NOTES TEXTBOOK READINGS PROBLEM SETS PROBLEM SOLVING HELP VIDEOS* IN-CLASS DEMONSTRATIONS
Periodic Oscillations, Harmonic Oscillators


Typed Notes for Lecture 1 (PDF)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 1 (PDF - 2.2MB)

 Chapter 1: Harmonic Oscillation (PDF - 1.4MB) Problem Set 1 (PDF) Simple Harmonic Motion and Introduction to Problem Solving

Air Cart Between Springs

Mass on a Spring

Two Pendulums with Different Amplitudes
Damped Free Oscillators


Typed Notes for Lecture 2 (PDF)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 2 (PDF - 2MB)

 Chapter 2: Forced Oscillation and Resonance (PDF - 1.3MB) None None

Oscillating Steel Ball on a Track

Physical Pendulum

Damped and Undamped Masses on a Spring

Driven Torsional Balance Oscillator
Driven Oscillators, Transient Phenomena, Resonance


This resource may not render correctly in a screen reader.Typed Notes for Lecture 3 (PDF - 1.2MB)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 3 (PDF - 2.1MB)

 Chapter 2: Forced Oscillation and Resonance (PDF - 1.3MB) Problem Set 2 (PDF)

Harmonic Oscillators with Damping

Driven Harmonic Oscillators

Coupled Oscillators without Damping

Driven Cart on Air Track

Driven Mechanical Oscillator

Breaking Glass with Sound
Coupled Oscillators, Normal Modes


Typed Notes for Lecture 4 (PDF)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 4 (PDF - 2.7MB)

 Chapter 3: Normal Modes (PDF - 1.4MB) None None

Double Pendulum

Weighted Hacksaw Blade

Two Rigid Pendulums Coupled with a Spring

Two Pendulums Coupled with a Rod

Wilberforce Pendulum
Beat Phenomena


This resource may not render correctly in a screen reader.Typed Notes for Lecture 5 (PDF - 1.1MB)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 5 (PDF - 1.7MB)

 Chapter 3: Normal Modes (PDF - 1.4MB) Problem Set 3 (PDF) Coupled Oscillators without Damping

Two Rigid Pendulums Coupled with a Spring

Wave Beats

Coupled Tunning Forks
Driven Oscillators, Resonance


This resource may not render correctly in a screen reader.Typed Notes for Lecture 6 (PDF - 1.3MB)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 6 (PDF - 1.5MB)

Chapter 4: Symmetries (PDF - 1.3MB)

Chapter 5: Waves (PDF - 1.4MB) (through section 5.2)

 None None

Two Rigid Pendulums Coupled with a Spring

Coupled Air Carts
Symmetry, Infinite Number of Coupled Oscillators


This resource may not render correctly in a screen reader.Typed Notes for Lecture 7 (PDF - 1.1MB)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 7 (PDF - 1.9MB)

 Chapter 4: Symmetries (PDF - 1.3MB)

Chapter 5: Waves (PDF - 1.4MB) (through section 5.2)

 Problem Set 4 (PDF)

Standing Waves Part I

Standing Waves Part II

Bell Labs Wave Machine

Vibrating Spring (Hand Driven)
Translation Symmetry


This resource may not render correctly in a screen reader.Typed Notes for Lecture 8 (PDF - 1.2MB)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 8 (PDF - 1.9MB)

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)

 None None Bell Labs Wave Machine
Wave Equation, Standing Waves, Fourier Series


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)

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 5 (PDF)

Traveling Waves without Damping

Standing Waves Part I

Standing Waves Part II

Bell Labs Wave Machine

Rijke Tube
Exam 1 (covers Lecture 1 through Lecture 8) (no video)

**What you should know:

 How to write down Equation of Motion
 Undamped, under-damped, critically damped, over-damped
* Driven oscillator, transient behavior and steady state solution, resonance
* How to determine the unknown coefficients using initial conditions
* Coupled systems: What are the normal modes? How to solve M-1K eigenvalue problems and what are the full solutions? Driven coupled oscillator, resonance
* Symmetry & Infinite coupled system: What is the solution of reflection and translation symmetric system? How to determine the dispersion relation ω(k)?

This resource may not render correctly in a screen reader.Exam 1 Formula Sheet (PDF)

Practice Exam 1 (PDF)

This resource may not render correctly in a screen reader.Practice Exam 1 Solution (PDF)
Traveling Waves


This resource may not render correctly in a screen reader.Typed Notes for Lecture 10 (PDF - 1.9MB)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 10 (PDF - 2.4MB)

Chapter 6: Continuum Limit and Fourier Series (PDF - 1.2MB) (section 6.2 to end)

Chapter 7: Longitudinal Oscillations and Sound (PDF - 1.3MB)

Chapter 8: Traveling Waves (PDF - 1.4MB) (through section 8.2)

 None None Bell Labs Wave Machine (Mismatched Impedance)
Sound Waves


This resource may not render correctly in a screen reader.Typed Notes for Lecture 11 (PDF - 1.2MB)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 11 (PDF - 2.4MB)

Chapter 6: Continuum Limit and Fourier Series (PDF - 1.2MB) (section 6.2 to end)

Chapter 7: Longitudinal Oscillations and Sound (PDF - 1.3MB)

Chapter 8: Traveling Waves (PDF - 1.4MB) (through section 8.2)

 Problem Set 6 (PDF) Electromagnetic Waves in a Vacuum

Standing Sound Waves in a Glass Tube

Helium Balloon

Part II: Electromagnetic Waves

TITLE LECTURE VIDEOS LECTURE NOTES TEXTBOOK READINGS PROBLEM SETS PROBLEM SOLVING HELP VIDEOS* IN-CLASS DEMONSTRATIONS
Maxwell’s Equation, Electromagnetic Waves


This resource may not render correctly in a screen reader.Typed Notes for Lecture 12 (PDF - 2.6MB)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 12 (PDF - 3MB)

Chapter 8: Traveling Waves (PDF - 1.4MB) (section 8.3 to end)

Chapter 9: The Boundary at Infinity (PDF - 1.3MB) (through section 9.2)

 None Electromagnetic Waves in a Vacuum None
Dispersive Medium, Phase Velocity, Group Velocity


This resource may not render correctly in a screen reader.Typed Notes for Lecture 13 (PDF - 1.1MB)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 13 (PDF - 1.9MB)

Chapter 8: Traveling Waves (PDF - 1.4MB) (section 8.3 to end)

Chapter 9: The Boundary at Infinity (PDF - 1.3MB) (through section 9.2)

 Problem Set 7 (PDF) Accelerated Charges Radiating Electromagnetic Waves Bell Labs Wave Machine
Fourier Transform, AM Radio


This resource may not render correctly in a screen reader.Typed Notes for Lecture 14 (PDF - 1.3MB)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 14 (PDF - 2.7MB)

 Chapter 10: Signals and Fourier Analysis (PDF - 1.4MB) None None None
Uncertainty Principle, 2D Waves


This resource may not render correctly in a screen reader.Typed Notes for Lecture 15 (PDF - 1.2MB)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 15 (PDF - 2.2MB)

 Chapter 10: Signals and Fourier Analysis (PDF - 1.4MB) Problem Set 8 (PDF) Interference of Electromagnetic Waves Chladni Figures (Speaker Driven)
2D and 3D Waves, Snell’s Law


This resource may not render correctly in a screen reader.Typed Notes for Lecture 16 (PDF - 1.8MB)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 16 (PDF - 2.6MB)

Chapter 11: Two and Three Dimensions (PDF - 1.8MB)

Chapter 12: Polarization (PDF - 1.4MB) (through section 12.3)

 None None

Chladni Figures (Speaker Driven)

Oscillating Soap Film

Part III: Optics

TITLE LECTURE VIDEOS LECTURE NOTES TEXTBOOK READINGS PROBLEM SETS PROBLEM SOLVING HELP VIDEOS* IN-CLASS DEMONSTRATIONS
Polarization, Polarizer


This resource may not render correctly in a screen reader.Typed Notes for Lecture 17 (PDF - 1.2MB)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 17 (PDF - 2MB)

Chapter 11: Two and Three Dimensions (PDF - 1.8MB)

Chapter 12: Polarization (PDF - 1.4MB) (through section 12.3)

 None None

Total Internal Reflection

Fiber Optic Bundle

Polarization of Microwaves
Exam 2 (covers Lecture 9 through Lecture 16) (no video)

**What you should know:

 How to use infinite system to solve finite system
 Continues limit: Wave equations!
* Solutions to wave equations: Normal modes (Progressing wave solutions standing waves)
* Matching the boundary of two systems: Reflection and transmission
* Longitudinal waves: Spring waves and sound waves
* EM waves: How to calculate electric field and magnetic field from one another, standing EM waves, energy density and Poynting vector
* Dispersive medium: Dispersive relation, Fourier transform, AM radio and Uncertainty Principle
* 2D and 3D waves: Normal modes, Snell’s Law

This resource may not render correctly in a screen reader.Exam 2 Formula Sheet (PDF - 1.2MB)

Practice Exam 2 (PDF)

This resource may not render correctly in a screen reader.Practice Exam 2 Solution (PDF)
Wave Plates, Radiation


This resource may not render correctly in a screen reader.Typed Notes for Lecture 18 (PDF - 2.2MB)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 18 (PDF - 2.2MB)

 Chapter 12: Polarization (PDF - 1.4MB) (section 12.4 to end) None None

Polarizing Filters and Light

Polarization in a Sugar Solution

Polarization of Radio Waves (Dipole Antenna)
Waves in Medium


This resource may not render correctly in a screen reader.Typed Notes for Lecture 19 (PDF)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 19 (PDF - 1.9MB)

 Chapter 12: Polarization (PDF - 1.4MB) (section 12.4 to end) Problem Set 9 (PDF) None Brewster’s Angle
Interference, Soap Bubble


Typed Notes for Lecture 20 (PDF)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 20 (PDF - 1.6MB)

 Chapter 13: Interference and Diffraction (PDF - 1.6MB) Problem Set 10 (PDF)

Accelerated Charges Radiating Electromagnetic Waves

Interference of Electromagnetic Waves

Reflection off Soap Bubbles

Reflection off a Soap Film
Phased Radar, Single Electron Interference


This resource may not render correctly in a screen reader.Typed Notes for Lecture 21 (PDF - 3.2MB)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 21 (PDF - 1.8MB)

 Chapter 13: Interference and Diffraction (PDF - 1.6MB) None None

Ripple Tank (Interference of Two Point Sources)

Moiré Pattern

Single-Slit Diffraction with a Laser
Diffraction, Resolution


Typed Notes for Lecture 22 (PDF)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 22 (PDF - 2MB)

 Chapter 13: Interference and Diffraction (PDF - 1.6MB) None None Single-Slit Diffraction with a Laser
Quantum Waves and Gravitational Waves


This resource may not render correctly in a screen reader.Typed Notes for Lecture 23 (PDF - 1.2MB)

This resource may not render correctly in a screen reader.Handwritten Notes for Lecture 23 (PDF - 4.6MB)

 None None None None
Review for Final Exam
None None None None None

Final Exam (covers Lecture 1 through Lecture 23)

FORMULA SHEET PRACTICE FINAL EXAMS SOLUTIONS
This resource may not render correctly in a screen reader.Final Exam Formula Sheet (PDF)

Practice Final Exam 1 (PDF)

This resource may not render correctly in a screen reader.Practice Final Exam 2 (PDF - 1.3MB)

Practice Final Exam 3 (PDF)

This resource may not render correctly in a screen reader.Practice Final Exam 1 Solution (PDF - 1.3MB)

This resource may not render correctly in a screen reader.Practice Final Exam 2 Solution (PDF)

This resource may not render correctly in a screen reader.Practice Final Exam 3 Solution (PDF)

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

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