HARMONICS --- Session III of the Mathematics
and Science Institutes for DCPS Middle School Teachers
You are HERE --- http://www.carnegieinstitution.org/first_light_case/horn/MSI/harmonicsmsi.html
|
Harmonics are modes of vibrations that begin with the lowest or fundamental frequency and continue as a sequence of tones that are integral (means whole numbers) multiples of the fundamental frequency. Frequency for a vibrating object. Number of vibrations per unit time. Frequency is proportional to the reciprocal of the length. Frequency is proportional to the square root of the tension. Pitch. The shrillness of the sound. Waves. The number of waves that pass through a particular point per (ratio and proportion) unit time. SOUND (GSU Hyperphysics web site) vibrations harmonica harmony harmonic scale mathematics |
Periodicity. A sine wave is the simples.t of waves with a single frequency (Fourier). --- Looking for periodicity. What is a periodicity transform? communication Resonance. Resonance and natural frequency. Tacoma Narrows Bridge Collapse. Instruments (sound waves and music) band orchestra |
radio CD syncopation pleasant physics organization guitar harmonic scale strum |
Waves
What is a wave?
Three different ways of visualizing a wave...
Resonance
Waves
Doppler effect and here
Sonic boom --- and--- what a sonic boom LOOKS like
Quantum wave packets animation (toby's subscription to JCE online) scroll to harmonic oscillator
Sine wave generators
Real world applications
http://grape.c.u-tokyo.ac.jp/~hachisu/java.shtml
How we hear
Example Lessons
Maxwell
Hertz the experiment testing the equivalence of electromagnetic waves and light video of Hertz's experimental device
Marconi
A proportion is the equality of two ratios: a=kb, a/b=k, a/b=k/1
Digital oscilloscope (free software for PC)
Physics demonstrations and here