View source for Hertz

{{short description|SI unit for frequency}}

{{Infobox unit
| name = Hertz
| image =
| caption =
| standard = [[SI derived unit]]
| quantity = [[Physics:Frequency|Frequency]]
| symbol = Hz
| dimension = T<sup>−1</sup>
| namedafter = [[Biography:Heinrich Hertz|Heinrich Hertz]]
| extralabel = In [[SI base unit]]s
| extradata = [[Second|s]]<sup>−1</sup>
}}
[[File:FrequencyAnimation.gif|thumb|upright=1.05|Top to bottom: Lights flashing at [[Physics:Frequency|frequencies]] {{nowrap|''f'' {{=}} 0.5 Hz}}, 1.0&nbsp;Hz and 2.0&nbsp;Hz, i.e.&nbsp;at 0.5, 1.0 and 2.0 flashes per second, respectively. The time between each flash –&nbsp;the ''period''&nbsp;T&nbsp;– is given by {{frac|1|''f''}} (the [[Multiplicative inverse|reciprocal]] of ''f''{{px1}}), i.e. 2, 1 and 0.5 seconds, respectively.]]

The '''hertz''' (symbol: '''Hz''') is the [[SI derived unit|derived unit]] of [[Physics:Frequency|frequency]] in the [[International System of Units]] (SI) and is defined as one [[Physics:Cycle per second|cycle per second]].<ref>"hertz". (1992). ''American Heritage Dictionary of the English Language'' (3rd ed.), Boston: Houghton Mifflin.</ref> It is named after [[Biography:Heinrich Hertz|Heinrich Rudolf Hertz]], the first person to provide conclusive proof of the existence of electromagnetic waves. Hertz are commonly expressed in [[Metric prefix|multiples]]: kilohertz (10<sup>3</sup> Hz, kHz), megahertz (10<sup>6</sup> Hz, MHz), gigahertz (10<sup>9</sup> Hz, GHz), terahertz (10<sup>12</sup> Hz, THz), petahertz (10<sup>15</sup> Hz, PHz),  exahertz (10<sup>18</sup> Hz, EHz),
and zettahertz (10<sup>21</sup> Hz, ZHz).

Some of the unit's most common uses are in the description of [[Physics:Sine wave|sine wave]]s and [[Musical tone|musical tone]]s, particularly those used in radio- and audio-related applications. It is also used to describe the clock speeds at which computers and other electronics are driven. The units are sometimes also used as a representation of energy, via the [[Physics:Photon energy|photon energy]] equation (''E''=''h''&nu;), with one hertz equivalent to ''[[Physics:Planck constant|h]]'' joules.

== Definition ==
The hertz is defined as one [[Physics:Cycle per second|cycle per second]]. The [[Organization:International Committee for Weights and Measures|International Committee for Weights and Measures]] defined the [[Second|second]] as "the duration of 9&nbsp;192&nbsp;631&nbsp;770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the [[Chemistry:Caesium|caesium]]-133 atom"<ref>  {{cite web
 | url = http://www.bipm.org/en/si/si_brochure/chapter2/2-1/second.html
 | title = SI brochure: Table 3. Coherent derived units in the SI with special names and symbols
}}</ref><ref>{{cite web
 | url = http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf
 | title = [Resolutions of the] CIPM, 1964 – Atomic and molecular frequency standards
 | publisher = SI brochure, Appendix 1
}}</ref> and then adds: "It follows that the hyperfine splitting in the ground state of the caesium 133 atom is exactly 9&nbsp;192&nbsp;631&nbsp;770 hertz, ν(hfs Cs) = 9&nbsp;192&nbsp;631&nbsp;770 Hz." The dimension of the unit hertz is 1/time (1/T). Expressed in base SI units it is 1/second (1/s). Problems can arise because the units of angular measure (cycle or radian) are omitted in SI.<ref>{{cite journal | last1 = Mohr | first1 = J. C. | last2 = Phillips | first2 = W. D. | year = 2015 | title = Dimensionless Units in the SI | url = | journal = Metrologia | volume = 52 | issue = 1 | pages = 40–47 | doi = 10.1088/0026-1394/52/1/40 | bibcode = 2015Metro..52...40M | arxiv = 1409.2794 }}</ref><ref>{{cite journal | last1 = Mills | first1 = I. M. | year = 2016 | title = On the units radian and cycle for the quantity plane angle | url = | journal = Metrologia | volume = 53 | issue = 3 | pages = 991–997 | doi = 10.1088/0026-1394/53/3/991 | bibcode = 2016Metro..53..991M }}</ref><ref>{{cite journal | title = SI units need reform to avoid confusion | journal = Nature | department = Editorial | date = 7 August 2011 | volume = 548 | issue = 7666 | page = 135 | doi = 10.1038/548135b| pmid = 28796224 | doi-access = free }}</ref><ref>{{cite journal
|author1=P. R. Bunker |author2=I. M. Mills |author3=Per Jensen 
| title = The Planck constant and its units	
| journal = J Quant Spectrosc Radiat Transfer
| volume = 237 | page= 106594 | year = 2019
| doi = 10.1016/j.jqsrt.2019.106594 |bibcode=2019JQSRT.23706594B }}</ref> 

In English, "hertz" is also used as the plural form.<ref>[http://physics.nist.gov/Pubs/SP811/sec09.html NIST Guide to SI Units – 9 Rules and Style Conventions for Spelling Unit Names], National Institute of Standards and Technology</ref> As an SI unit, Hz can be [[Metric prefix|prefixed]]; commonly used multiples are kHz (kilohertz, 10<sup>3</sup>&nbsp;Hz), MHz (megahertz, 10<sup>6</sup>&nbsp;Hz), GHz (gigahertz, 10<sup>9</sup>&nbsp;Hz) and THz (terahertz, 10<sup>12</sup>&nbsp;Hz). One hertz simply means "one cycle per [[Second|second]]" (typically that which is being counted is a complete cycle); 100&nbsp;Hz means "one hundred cycles per second", and so on. The unit may be applied to any periodic event—for example, a clock might be said to tick at 1&nbsp;Hz, or a human heart might be said to [[Heart rate|beat]] at 1.2&nbsp;Hz. 

The occurrence [[Aperiodic frequency|rate of aperiodic]] or [[Stochastic|stochastic]] events is expressed in '''reciprocal second''' or '''inverse second''' (1/s or s<sup>−1</sup>) in general or, in the specific case of [[Physics:Radioactive decay|radioactive decay]], in [[Becquerel|becquerel]]s.<ref name="BIPMtable3">"(d) The hertz is used only for periodic phenomena, and the becquerel (Bq) is used only for stochastic processes in activity referred to a radionuclide." {{cite web |url=http://www.bipm.org/en/publications/si-brochure/section2-2.html#section2-2-2 |title=BIPM – Table 3 |publisher=BIPM | accessdate=2012-10-24}}</ref> Whereas 1&nbsp;Hz is 1 [[Physics:Cycle per second|cycle per second]], 1 Bq is 1 aperiodic radionuclide event per second.

Even though [[Physics:Angular velocity|angular velocity]], [[Physics:Angular frequency|angular frequency]] and the unit hertz all have the dimension 1/s, angular velocity and angular frequency are not expressed in hertz,<ref>{{cite web
 |url=http://www.bipm.org/en/si/derived_units/2-2-2.html 
 |title=SI brochure, Section 2.2.2, paragraph 6 
 |url-status=dead 
 |archiveurl=https://web.archive.org/web/20091001192328/http://www.bipm.org/en/si/derived_units/2-2-2.html 
 |archivedate=1 October 2009 
 |df=dmy-all 
}}</ref> but rather in an appropriate angular unit such as radians per second. Thus a disc rotating at 60 revolutions per minute (rpm) is said to be rotating at either 2{{pi}}&nbsp;rad/s ''or'' 1&nbsp;Hz, where the former measures the [[Physics:Angular velocity|angular velocity]] and the latter reflects the number of ''complete'' revolutions per second. The conversion between a frequency ''f'' measured in hertz and an angular velocity ''ω'' measured in radians per second is
:<math>
\omega = 2\pi f \,</math> and <math>f = \frac{\omega}{2\pi} \,
</math>.

{{SI unit lowercase|Heinrich Hertz|hertz|Hz}}

==History==
The hertz is named after the German physicist [[Biography:Heinrich Hertz|Heinrich Hertz]] (1857–1894), who made important scientific contributions to the study of [[Physics:Electromagnetism|electromagnetism]]. The name was established by the [[Organization:International Electrotechnical Commission|International Electrotechnical Commission]] (IEC) in 1930.<ref>{{cite web|url=http://www.iec.ch/about/history/overview/ |title=IEC History |publisher=Iec.ch |date=1904-09-15 |accessdate=2012-04-28}}</ref> It was adopted by the [[General Conference on Weights and Measures]] (CGPM) (''Conférence générale des poids et mesures'') in 1960, replacing the previous name for the unit, ''[[Physics:Cycle per second|cycles per second]]'' (cps), along with its related multiples, primarily ''kilocycles per second'' (kc/s) and ''megacycles per second'' (Mc/s), and occasionally ''kilomegacycles per second'' (kMc/s). The term ''cycles per second'' was largely replaced by ''hertz'' by the 1970s. One hobby magazine, ''Electronics Illustrated'', declared their intention to stick with the traditional kc., Mc., etc. units.<ref>{{cite magazine
|last=Cartwright |first=Rufus |date=March 1967 |title=Will Success Spoil Heinrich Hertz? |URL=http://www.americanradiohistory.com/Archive-Electronics-Illustrated/Electronics-Illustrated-1967-03.pdf |magazine=Electronics Illustrated |pages=98–99 |publisher=Fawcett Publications, Inc. |editor-last=Beason |editor-first=Robert G.}}</ref>

==Applications==
[[File:Wave frequency.gif|thumb|upright=1.8|A [[Physics:Sine wave|sine]] <ref>{{Cite journal|last=Rekdal|first=Ole Bjørn|date=2014-08-01|title=Academic urban legends|journal=Social Studies of Science|volume=44|issue=4|pages=638–654|doi=10.1177/0306312714535679|issn=0306-3127|pmc=4232290|pmid=25272616}}</ref>wave with varying frequency]]
[[File:Wiggers Diagram.svg|thumb|upright=1.8|A heartbeat is an example of a non-sinusoidal periodic phenomenon that may be analyzed in terms of frequency. Two cycles are illustrated.]]

===Vibration===
[[Physics:Sound|Sound]] is a traveling [[Physics:Longitudinal wave|longitudinal wave]] which is an oscillation of [[Physics:Pressure|pressure]]. Humans perceive frequency of sound waves as [[Physics:Pitch (music)|pitch]]. Each musical note corresponds to a particular frequency which can be measured in hertz. An infant's ear is able to perceive frequencies ranging from 20&nbsp;Hz to 20,000&nbsp;Hz; the average [[Biology:Adult|adult human]] can hear sounds between 20&nbsp;Hz and 16,000&nbsp;Hz.<ref>{{cite web|author=Ernst Terhardt |url=http://www.mmk.e-technik.tu-muenchen.de/persons/ter/top/dominant.html |title=Dominant spectral region |publisher=Mmk.e-technik.tu-muenchen.de |date=2000-02-20 |accessdate=2012-04-28 |url-status=dead |archiveurl=https://web.archive.org/web/20120426090422/http://www.mmk.e-technik.tu-muenchen.de/persons/ter/top/dominant.html |archivedate=26 April 2012 |df=dmy-all }}</ref> The range of [[Physics:Ultrasound|ultrasound]], [[Physics:Infrasound|infrasound]] and other physical vibrations such as [[Physics:Molecular vibration|molecular]] and [[Physics:Atom vibrations|atomic vibrations]] extends from a few femtohertz<ref>{{cite web|url=https://science.nasa.gov/science-news/science-at-nasa/2003/09sep_blackholesounds/|title=Black Hole Sound Waves - Science Mission Directorate|publisher=science.nasa.go}}</ref> into the [[Tera-|tera]]hertz range<ref>[[Physics:Atom vibrations|Atomic vibrations]] are typically on the order of tens of terahertz</ref> and beyond.

==={{anchor|Electricity}} Electromagnetic radiation===
[[Physics:Electromagnetic radiation|Electromagnetic radiation]] is often described by its frequency—the number of [[Oscillation|oscillation]]s of the perpendicular electric and magnetic fields per second—expressed in hertz.

Radio frequency radiation is usually measured in kilohertz (kHz), megahertz (MHz), or gigahertz (GHz). [[Physics:Light|Light]] is electromagnetic radiation that is even higher in frequency, and has frequencies in the range of tens ([[Physics:Infrared|infrared]]) to thousands ([[Physics:Ultraviolet|ultraviolet]]) of terahertz. Electromagnetic radiation with frequencies in the low terahertz range (intermediate between those of the highest normally usable radio frequencies and long-wave infrared light) is often called [[Physics:Terahertz radiation|terahertz radiation]]. Even higher frequencies exist, such as that of [[Physics:Gamma ray|gamma ray]]s, which can be measured in exahertz (EHz). (For historical reasons, the frequencies of light and higher frequency electromagnetic radiation are more commonly specified in terms of their [[Wavelength|wavelength]]s or [[Physics:Photon|photon]] [[Physics:Energy|energies]]: for a more detailed treatment of this and the above frequency ranges, see [[Physics:Electromagnetic spectrum|electromagnetic spectrum]].)

===Computers===
{{details|topic=why the frequency, including for gigahertz (GHz) etc., is a flawed speed indicator for computers|Megahertz myth}}
In computers, most [[Central processing unit|central processing unit]]s (CPU) are labeled in terms of their [[Clock rate|clock rate]] expressed in megahertz (10<sup>6</sup> Hz) or gigahertz (10<sup>9</sup> Hz). This specification refers to the frequency of the CPU's master [[Engineering:Clock signal|clock signal]]. This signal is a [[Square wave|square wave]], which is an electrical voltage that switches between low and high logic values at regular intervals. As the hertz has become the primary unit of measurement accepted by the general populace to determine the performance of a CPU, many experts have criticized this approach, which they claim is an [[Engineering:Megahertz myth|easily manipulable benchmark]]. Some processors use multiple clock periods to perform a single operation, while others can perform multiple operations in a single cycle.<ref>{{cite magazine|first=Amit |last=Asaravala |url=https://www.wired.com/news/business/0,1367,62851,00.html |title=Good Riddance, Gigahertz |magazine=Wired |date=2004-03-30 |accessdate=2012-04-28}}</ref> For personal computers, CPU clock speeds have ranged from approximately 1&nbsp;MHz in the late 1970s ([[Company:Atari|Atari]], [[Company:Commodore International|Commodore]], Apple computers) to up to 6&nbsp;GHz in [[Engineering:IBM POWER microprocessors|IBM POWER microprocessors]].

Various [[Engineering:Bus (computing)|computer buses]], such as the [[Engineering:Front-side bus|front-side bus]] connecting the CPU and northbridge, also operate at various frequencies in the megahertz range.

== {{Visible anchor|SI multiples}} == <!-- Other articles link here. -->
{{SI multiples
| symbol=Hz
| unit=hertz
| note=Common prefixed units are in bold face.
| k=10<sup>3</sup> s|M=10<sup>6</sup> s|G=10<sup>9</sup> s|T=10<sup>12</sup> s|
| anchor=SI_prefixed_forms_of_hertz
| right=
}}

Higher frequencies than the [[International System of Units]] provides prefixes for are believed to occur naturally in the frequencies of the quantum-mechanical vibrations of high-energy, or, equivalently, massive particles, although these are not directly observable and must be inferred from their interactions with other phenomena. By convention, these are typically not expressed in hertz, but in terms of the equivalent quantum energy, which is proportional to the frequency by the factor of [[Physics:Planck constant|Planck's constant]].

{| class="wikitable"
! colspan="3" style="font-weight:bold;" |Hertz: Unicode characters.<ref name="Unicode-U3300">{{cite web |url=https://www.unicode.org/charts/PDF/U3300.pdf |access-date=May 24, 2019 |title=The Unicode Standard 12.0 – CJK Compatibility ❰ Range: 3300—33FF ❱ |author=Unicode Consortium |date=2019 |website=Unicode.org}}</ref>
|-
| style="font-weight:bold;" | Symbol
| style="font-weight:bold;" | Name
| style="font-weight:bold;" | Unicode number
|-
| ㎐
| Hertz (Square HZ)
| U+3390
|-
| ㎑
| Kilohertz (Square KHZ)
| U+3391
|-
| ㎒
| Megahertz (Square MHZ)
| U+3392
|-
| ㎓
| Gigahertz (Square GHZ)
| U+3393
|-
| ㎔
| Terahertz (Square THZ)
| U+3394
|}

== See also ==
* [[Physics:Alternating current|Alternating current]]
* [[Bandwidth (signal processing)]]
* [[Engineering:Electronic tuner|Electronic tuner]]
* [[FLOPS]]
* [[Engineering:Frequency changer|Frequency changer]]
* Normalized frequency
* [[Orders of magnitude (frequency)]]
* [[Periodic function]]
* [[Radian per second]]
* [[Rate (mathematics)|Rate]]
* [[CJK Compatibility|Unicode CJK Compatibility block]] which includes common SI units for frequency

== Notes and references ==
{{Reflist|30em}}

==External links==
* [http://www.bipm.org/en/si/si_brochure/chapter2/2-1/second.html SI Brochure: Unit of time (second)]
* [https://nrc.canada.ca/en/stories/accuracy-single-ion-clock-pushed-new-limits National Research Council of Canada: ''Cesium fountain clock'']
* [https://web.archive.org/web/20131223133059/http://archive.nrc-cnrc.gc.ca/eng/projects/inms/trapped-ion.html National Research Council of Canada: ''Optical frequency standard based on a single trapped ion'']
* [https://web.archive.org/web/20130627155632/http://archive.nrc-cnrc.gc.ca/eng/projects/inms/optical-comb.html National Research Council of Canada: ''Optical frequency comb'']
* [https://www.npl.co.uk/time-frequency/optical-atomic-clocks National Physical Laboratory: ''Time and frequency Optical atomic clocks'']
* [http://onlinetonegenerator.com Online Tone Generator]

{{SI units}}

[[Category:SI derived units]]
[[Category:Units of frequency]]

{{Sourceattribution|Hertz}}