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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.
University of Guelph
University of Guelph: Physics Tutorials: Amplitude, Period, and Frequency
A tutorial describing the characteristics of simple harmonic motion. Utilizes animations, mathematical equations, and interactive questions to teach essential principles.
Physics Classroom
The Physics Classroom: Wave: Mathematics of Standing Waves
Students analyze harmonic patterns through several example problems and interactive practice examples.
Khan Academy
Khan Academy: Standing Waves Review
Review key terms and skills related to standing waves including how to find standing wave harmonics.
University of New South Wales (Australia)
Univ of New South Wales: Musical Acoustics: Strings, Standing Waves, Harmonics
The production of a standing wave in a string is presented and discussed in this site. Exceptional diagrams are accompanied by thorough explanation and mathematical analysis to explain the various modes of vibrations.
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...
Other
Harmonic Analysis of Debussy's Prelude La Fille Aux Cheveux De Lin (Book I,viii)
A fine analysis of this Debussy prelude. Diagrams and text are easy to understand. The online sound clips are a plus! Site also available in Spanish.
Concord Consortium
Concord Consortium: Molecular Workbench Showcase: Quantum Harmonic Oscillator
Understand classic correspondence, coherent and squeezed states, quantum transitions, and quantum dissipation in this animation. Get a foundation for quantum mechanics.
CK-12 Foundation
Ck 12 Exploration Series: Simulations: Physics: Violin
[Free Registration/Login Required] Learn about wave harmonics on a string by looking closely at the sound produced by a violin. Test string tension with harmonic number on violin strings in a simulated practice. Understand sound waves...
CK-12 Foundation
Ck 12 Exploration Series: Simulations: Physics: Pan Flute
[Free Registration/Login Required] A simulation to learn about wave harmonics in a column of air by looking closely at the sound produced by a pan flute.
University of Colorado
University of Colorado: Ph Et Interactive Simulations: Pendulum Lab
An interactive simulation that teaches about periodic motion, simple harmonic motion, and conservation of energy. Observe one or two pendulums to determine how the swing is influenced by the length of the string, the mass of the pendulum...
Music Theory
Music theory.net: The Minor Scales
Listen and learn with this explanation of minor scales. Each description of harmonic, melodic, and minor scales provides an illustrated example, and audio clips.
Music Theory
Music theory.net: Diatonic Triads
Descriptions of diatonic triads: major, natural minor, and harmonic minor. Provides animated illustrations, and a printable chart at the end of the lesson.
Texas Education Agency
Texas Gateway: Sound Interference and Resonance: Standing Waves in Air Columns
By the end of this section, you will be able to define antinode, node, fundamental, overtones, and harmonics; identify instances of sound interference in everyday situations; describe how sound interference occurring inside open and...
TeachEngineering
Teach Engineering: Into the Swing of Things
Students learn the basic properties of periodic and harmonic motion, and how the rearrangement of the simple pendulum equation can be used to solve for gravitational acceleration, pendulum length, and gravity. At lesson end, students are...
CK-12 Foundation
Ck 12: Mass on a Spring
[Free Registration/Login may be required to access all resource tools.] Students solve problems dealing with simple harmonic motion using a mass on a string.
Learn AP Physics
Learn Ap Physics: Physics B: Oscillatory Motion
A site dedicated to help students prepare for the AP Physics B test. This specific site reviews oscillatory motion including simple harmonic motion, Hooke's law, harmonic motion, pendulum, and springs. Site contains links to video...
Science Buddies
Science Buddies: Blowing Bottletops: Making Music With Glass Bottles
This is a musical project about the resonance of closed-end air columns. Organ pipes, flutes, and brass instruments are examples of musical instruments of this type. In this project, you'll learn how the pitch of the note produced...
Science Buddies
Science Buddies: Singing Wine Glasses
Making a glass sing is not always as easy as it looks. This project explains the science behind the interesting hobby. You will be asked how the amount of fluid within a glass affects its pitch.
Wolfram Research
Wolfram Science World: Cl Circuit
Shows how simple harmonic motion is used in a circuit comprised of an inductor and a capacitor. Includes detailed formula derivation utilizing calculus.
San Diego State University
Sd State: Elements of Music: Media, Genre, Form Texture
One of the elements of music is "Texture." This site gives the definition, which basically is the relationship between melodic and harmonic.
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,...
Open Curriculum
Open Curriculum: Vibrations
To understand the concept and properties of vibrations and periodic motions such as the Simple Harmonic motion.
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.
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