American Association of Physics Teachers
Com Padre Digital Library: Open Source Physics: Harmonics and Fourier Series
The downloadable interactive java simulation displays the sum of harmonics through a Fourier series to yield a new wave.
OpenStax
Open Stax: Catherine Schmidt Jones: Harmonic Series
Dealing with the harmonic series, this website goes into come detail concerning pitch, frequency and color. Test your knowledge with several self checking problems.
Wolfram Research
Wolfram Math World: Harmonic Series
This MathWorld site provides a general overview of the harmonic series.
Texas Instruments
Texas Instruments: Up and Down: Damped Harmonic Motion
In this activity, students' will use a motion detector to record the motion data for a plate bouncing at the end of a light spring, and analyze the data to determine frequency, period and amplitude. They will then find an appropriate...
Texas Instruments
Texas Instruments: Numb3 Rs: Maintaining Balance
Based off of the hit television show NUMB3RS, this lesson has students determine center of mass for a series of objects (approximate JENGA blocks), and then to push each level so that it "hangs over" the level below it. Following this,...
Other
The Equal Tempered Scale & Peculiarities of Piano Tuning
The author offers a complete explanation of the physics behind piano tuning and why piano tuning is an intricate process. Illustrations and graphs are included.
Other
Math Lair: The Harmonic Series
This resource defines the Harmonic Series and gives a proof of its divergence.
OpenStax
Open Stax: Catherine Schmidt Jones: Tuning Systems
Here is a good introduction to the various tuning systems. Topics covered are Tuning Based on the Harmonic Series, Pythagorean Intonation, Mean-tone System, Just Intonation and more. This is also available as a printable pdf file.
![North Western University: Series [Pdf] Unknown Type](https://d15y2dacu3jp90.cloudfront.net/images/attachment_defaults/resource/large/FPO-knovation.png "North Western University: Series [Pdf] Unknown Type")
Northwestern University
North Western University: Series [Pdf]
The definition of a series is provided in a PDF document. The document also details the geometric, telescoping and harmonic series, tests for divergence, and series rules.
Math Open Reference
Math Open Reference: Integral Test
A handy reference guide to the integral test. It provides definitions, examples, and an animation that enhances further explanation. Includes links to related topics.
Math Open Reference
Math Open Reference: Series
A complete reference guide to a series. It provides definitions, examples, and an animation that enhances further explanation. Includes links to related topics.
Math Open Reference
Math Open Reference: Comparison Test
Learn about comparison tests with this helpful reference tool. Provides a detailed definition and examples that enhances further explanation. Includes links to related topics.
Other
Avatar Consultants, Inc: Tuning, Scales, and Temperament
A discussion of the composition of complex sounds produced by a musical instrument. Good illustration of how music is applied to physics. Quite a bit of good information, several pages linked together with good definitions as well as...
Interactive Mathematics
Interactive Mathematics: Line Spectrum
Using Fourier and Harmonic series, the line spectrums of functions are derived and represented on graphs. Several music examples show the connection between harmonics and sound.
Interactive Mathematics
Interactive Mathematics: Harmonic Analysis
Derived from the Fourier series, the harmonic series can be used to represent even and odd functions. Definitions of second and third harmonics are also provided.
Other
Math Pages: Bernoulli Numbers and Harmonic Series
This site from Math Pages contains information explaining harmonic series. The information is very in-depth and mathematic, but good factual information is provided. A good overall site.