Editing Pure tone

{{Short description|Sound with a sinusoidal waveform}}
[[File:Wave_sine.svg|right|thumb|A pure tone's pressure waveform versus time looks like this; its frequency determines the x axis scale; its amplitude determines the y axis scale; and its phase determines the x origin.]]

In [[psychoacoustics]], a '''pure tone''' is a sound with a [[sinusoidal]] [[waveform]]; that is, a [[sine]] [[wave]] of constant [[frequency]], [[phase-shift]], and [[amplitude]].<ref>[[ANSI S1.1-1994|ANSI S1.1-1994 Acoustical Terminology]]</ref>
By extension, in [[signal processing]] a single-frequency tone or pure tone is a purely sinusoidal [[signal]] (e.g., a voltage).
A pure tone has the property – unique among real-valued wave shapes – that its wave shape is unchanged by [[linear time-invariant system]]s; that is, only the phase and amplitude change between such a system's pure-tone input and its output.

Sine and cosine waves can be used as [[Basis function#Fourier basis|basic]] building blocks of more complex waves.  As additional sine waves having different frequencies are [[Superposition principle|combined]], the waveform transforms from a sinusoidal shape into a more complex shape.
When considered as part of a whole [[spectrum (physical sciences)|spectrum]], a pure tone may also be called a ''spectral component''.

In clinical [[audiology]], pure tones are used for [[pure-tone audiometry]] to characterize hearing thresholds at different frequencies.
[[Sound localization]] is often more difficult with pure tones than with other sounds.<ref>{{cite journal|author=Stanley Smith Stevens and Edwin B. Newman|title=The localization of actual sources of sound|journal=The American Journal of Psychology|date=1936|volume=48|issue=2|pages=297–306|doi=10.2307/1415748|jstor=1415748}}</ref><ref>{{cite journal|last1=Hartmann|first1=W. M.|title=Localization of sound in rooms|journal=The Journal of the Acoustical Society of America|date=1983|volume=74|issue=5|pages=1380–1391|doi=10.1121/1.390163|pmid=6643850|bibcode=1983ASAJ...74.1380H}}</ref>

== Relation to pitch and musical tones ==

Pure tones have been used by 19th century physicists like [[Georg Ohm]] and [[Hermann von Helmholtz]] to support theories asserting that the ear functions in a way equivalent to a [[Fourier analysis|Fourier frequency analysis]].<ref>{{cite book |last1=von Helmholtz |first1=Hermann L. F. |last2=Ellis |first2=Alexander J. |title=On the sensations of tone as a physiological basis for the theory of music |date=1875 |publisher=Longmans, Green, and Co. |location=London, UK |url=https://archive.org/stream/onsensationston00helmgoog#page/n2/mode/2up}}</ref><ref>{{cite journal |last1=Ohm |first1=Georg |title=Ueber die Definition des Tones, nebst daran geknupfter Theorie der Sirene und ahnlicher tonbildenden Vorrichtungen |journal=Poggendor's Annalen der Physik und Chemie |date=1843 |volume=59 |pages=513–565}}</ref> In [[Ohm's acoustic law]], later further elaborated by  Helmholtz, [[musical tone]]s are perceived as a set of pure tones. The percept of [[Pitch (music)|pitch]] depends on the frequency of the most prominent tone, and the phases of the individual components is discarded. This theory has often been blamed for creating a confusion between pitch, frequency and pure tones.<ref>{{cite book | title =  Foundations of Modern Auditory Theory | editor = Jerry V. Tobias | publisher = Academic Press | volume = 1 | author = W. Dixon Ward | chapter = Musical Perception |year = 1970 | page = 438}}</ref>

Unlike [[musical tone]]s that are composed of the sum of a number of harmonically related sinusoidal components, pure tones only contain one such sinusoidal waveform. When presented in isolation, and when its frequency pertains to a certain range, pure tones give rise to a single pitch percept, which can be characterized by its frequency. In this situation, the instantaneous phase of the pure tone varies linearly with time. If a pure tone gives rise to a constant, steady-state percept, then it can be concluded that its phase does not influence this percept. However, when multiple pure tones are presented at once, like in musical tones, their relative phase plays a role in the resulting percept. In such a situation, the perceived pitch is not determined by the frequency of any individual component, but by the frequency relationship between these components (see [[missing fundamental]]).<gallery>
File:Middle C, or 262 hertz, on a virtual oscilloscope.png|Pure tone [[Oscilloscope|oscillogram]] of middle C (262&nbsp;Hz). (Scale: 1 square is equal to 1 [[millisecond]])
File:C3 131 Hz oscillogram.png|Pure tone for C3, an [[octave]] below middle C. The frequency is half that of [[C (musical note)|middle C]] (131&nbsp;Hz).
File:C5 523 Hz oscillogram.png|Pure tone oscillogram of C5, an [[octave]] above middle C. The frequency is twice that of middle C (523&nbsp;Hz).
</gallery>

== See also ==
* [[Sound]]
* [[Pitch (music)]]
* [[Musical tone]]
* [[Missing fundamental]]
* [[Spectral flatness]]

== References ==
{{Reflist}}

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[[Category:Hearing]]
[[Category:Psychoacoustics]]
[[Category:Sound]]
[[Category:Acoustics]]
[[Category:Signal processing]]
[[Category:Spectrum (physical sciences)]]