Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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10 Harmonious Math



The amount of displacement, as measured from the still surface line, is called a wave's amplitude.


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Fourier Analysis

Fourier analysis is the process of taking a complicated signal and breaking it into sine and cosine components.

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Fourier Analysis and Synthesis

Fourier analysis breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite, constructing a complicated signal from simple sine waves.

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Whether or not we hear waves as sound has everything to do with their frequency, or how many times every second the molecules switch from compression to rarefaction and back to compression again, and their intensity, or how much the air is compressed.


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Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones

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Periodic Function

Trigonometric functions, such as sine and cosine, are useful for modeling sound waves, because they oscillate between values—they are periodic.

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Assuming that the air is of uniform density and pressure to begin with, a region of high pressure will be balanced by a region of low pressure, called rarefaction, immediately following the compression

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An instrument's tone, the sound it produces, is a complex mixture of waves of different frequencies.

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Wave Equation

The wave equation uses second derivatives to relate acceleration in space to acceleration in time.

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