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Sine Wave: Difference between revisions
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(Created page with "The Sine Wave or sinusoid is a mathematical curve that describes a smooth repetitive Oscillation. It is named after the function sine, of which it is the graph. It occ...") |
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The human ear can recognize single sine waves as sounding clear because sine waves are representations of a single frequency with no harmonics; some sounds that approximate a pure sine wave are whistling, a crystal glass set to vibrate by running a wet finger around its rim, and the sound made by a tuning fork. To the human ear, a sound that is made of more than one sine wave will have perceptible harmonics; addition of different sine waves results in a different waveform and thus changes the timbre of the sound. | The human ear can recognize single sine waves as sounding clear because sine waves are representations of a single frequency with no harmonics; some sounds that approximate a pure sine wave are whistling, a crystal glass set to vibrate by running a wet finger around its rim, and the sound made by a tuning fork. To the human ear, a sound that is made of more than one sine wave will have perceptible harmonics; addition of different sine waves results in a different waveform and thus changes the timbre of the sound. | ||
[[File:800px-Waveforms.svg.png|thumb|Sine, square, triangle, and sawtooth waveforms]] | |||
==Fourier series== | ==Fourier series== | ||
In 1822, French mathematician Joseph Fourier discovered that sinusoidal waves can be used as simple building blocks to describe and approximate any periodic waveform, including square waves. Fourier used it as an analytical tool in the study of waves and heat flow. It is frequently used in signal processing and the statistical analysis of time series. | In 1822, French mathematician Joseph Fourier discovered that sinusoidal waves can be used as simple building blocks to describe and approximate any periodic waveform, including square waves. Fourier used it as an analytical tool in the study of waves and heat flow. It is frequently used in signal processing and the statistical analysis of time series. | ||