Pure tone

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Pure tone

A pure tone is a tone with a sinusoidal waveshape.

A sine wave

Sine wave

The sine wave or sinusoid is a function that occurs often in mathematics, physics, signal processing, hearing , electrical engineering, and many other fields....
is characterized by its frequency — the number of cycles per second, or its wavelength
Wavelength

In physics, wavelength is the distance between repeating units of a propagating wave of a given frequency. It is commonly designated by the Greek language letter lambda ....
— the distance the waveform travels through its medium within a period, and the amplitude
Amplitude

Amplitude is the magnitude of change in the oscillating variable, with each oscillation, within an oscillating system. For instance, sound waves are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation....
— 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.

re sine wave is an artificial sound.

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Encyclopedia

A pure tone is a tone with a sinusoidal waveshape.

A sine wave

Sine wave

History

A pure sine wave is an artificial sound. Although some natural sounds may resemble it (e.g. the chirp of some birds) a pure sine wave had never been heard until it was created by man. Hermann von Helmholtz

Hermann von Helmholtz

Hermann Ludwig Ferdinand von Helmholtz was a Germany physician and physicist who made significant contributions to several widely varied areas of modern science....
is credited as the first creator of a sine wave with the 'Helmholtz siren

Siren (noisemaker)

A siren is a loud noise maker. The original version would yield sounds under water, suggesting a link with the sirens of Greek mythology. Most modern ones are civil defense siren or "air raid" sirens, tornado sirens, or the sirens on emergency service vehicles such as ambulances, police cars and Fire apparatus....
', 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 oscillator

Electronic oscillator

An electronic oscillator is an electronic circuit that produces a repetitive electronic signal, often a sine wave or a square wave.A low frequency oscillation is an electronic oscillator that generates an alternating current waveform at a frequency below ?200 Hz....
s.

Acoustic properties

Sinewaves are generally uncomfortable to the ear, and are more damaging to the ear than other noises at equal volumes. Sinewaves are often more difficult than other sounds at placing the location of its source- they seem to ‘fill the room’.

Fourier theorem

The Fourier theorem

Fourier theorem

In mathematics, the Fourier theorem is a theorem stating that a periodic function f, which is reasonably continuous function, may be expressed as the sum of a series of sine and cosine terms , each of which has specific amplitude and phase coefficients known as Fourier coefficients....
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

Harmonic series (mathematics)

In mathematics, the harmonic series is the Divergent series infinite series:Its name derives from the concept of overtones, or harmonics, in music: the wavelengths of the overtones of a vibrating string are 1/2, 1/3, 1/4, etc., of the string's fundamental wavelength....
and at specific phase

Phase (waves)

The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0....
relationships to each other.

The lowest of these frequencies (the fundamental frequency

Fundamental frequency

The fundamental tone, often referred to simply as the fundamental and abbreviated f0 or F0, is the lowest frequency in a harmonic series ....
), which is also the inverse of the period of the waveform, determines the pitch

Pitch (music)

Pitch represents the perceived fundamental frequency of a sound. It is one of the three major auditory system attributes of sounds along with loudness and timbre....
of the tone, which is perceived by the human hearing. In music, note

Note

In music, the term note has two primary meanings: 1) a sign used in musical notation to represent the relative duration and pitch of a sound; and 2) a pitched sound itself....
s are assigned to tones with different fundamental frequencies, in order to describe the pitch of played tones.