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# Pure tone

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### Pure tone

A pure tone is a tone with a sinusoidal waveform, i.e. a sine or cosine wave. This means that regardless of other characteristic properties such as amplitude or phase, the wave consists of a single frequency. Sine and cosine waves are the most basic building blocks of more complex waves, and as additional frequencies (i.e. additional sine and cosine waves having different frequencies) are combined, the waveform transforms from a sinusoidal into a more complex shape.

A sine wave is characterized by its frequency, the number of cycles per second—or its wavelength, the distance the waveform travels through its medium within a period—and the amplitude, the size of each cycle. A pure tone has the unique property that its waveshape and sound are changed only in amplitude and phase by linear acoustic systems.

A pure sine wave is an artificial sound. Hermann von Helmholtz is credited as the first creator of a sine wave, using the 'Helmholtz siren', a mechanical device that sends compressed air through holes in a rotating plate. This is presumably the closest thing to a sine wave that was heard before the invention of electronic oscillators.

Sine waves are generally uncomfortable to the ear, and may cause noise-induced hearing loss at lower volumes than other noises. Sound localization is often more difficult with sine waves than with other sounds; they seem to ‘fill the room’.

## Fourier theorem

The Fourier theorem states that any periodic waveform can be approximated as closely as desired as the sum of a series of sine waves with frequencies in a harmonic series and at specific phase relationships to each other.

The lowest of these frequencies (the fundamental frequency), which is also the inverse of the period of the waveform, determines the pitch of the tone, which is perceived by the human hearing. In music, notes are assigned to tones with different fundamental frequencies, in order to describe the pitch of played tones.

• Pure tones & complex sounds
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