View source for Hertz

{{short description|SI unit of frequency}}
{{About|the unit measure|the car rental company|Hertz Global Holdings|the surname|Hertz (name)|other uses}}
{{redirect-multi|2|Hz|Megahertz}}
{{Use dmy dates|date=May 2015}}
{{Infobox unit
| name = hertz
| image = FrequencyAnimation.gif
| caption = Top to bottom: Lights flashing at [[Frequency|frequencies]] {{nowrap|''f'' {{=}} {{val|0.5|u=Hz}}}}, {{val|1.0|u=Hz}} and {{val|2.0|u=Hz}}; that is,&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}}); that is, 2, 1 and 0.5 seconds, respectively.
| standard = [[SI]]
| quantity = [[frequency]]
| symbol = Hz
| dimension = T<sup>−1</sup>
| namedafter = [[Heinrich Hertz]]
| extralabel = In [[SI base unit]]s
| extradata = [[Inverse second|s<sup>−1</sup>]]
}}

The '''hertz''' (symbol: '''Hz''') is the unit of [[frequency]] in the [[International System of Units]] (SI), often described as being equivalent to one event (or [[Cycle per second|cycle]]) per [[second]].<ref>"hertz". (1992). ''American Heritage Dictionary of the English Language'' (3rd ed.), Boston: Houghton Mifflin.</ref>{{efn|Although hertz is often said to imply cycle per second (cps), the SI explicitly states that "cycle" and "cps" are not units in the SI, likely due to ambiguity in the terms.<ref name="SI Brochure 9">{{cite web |title=SI Brochure: The International System of Units (SI) – 9th edition |publisher=BIPM |page=26 |url=https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf |access-date=7 August 2022}}</ref>}} The hertz is an [[SI derived unit]] whose formal expression in terms of [[SI base unit]]s is 1/s or s<sup>−1</sup>, meaning that one hertz is one per second or the [[Inverse second|reciprocal of one second]].<ref name="SI Brochure 9" /> It is used only in the case of periodic events. It is named after [[Heinrich Hertz|Heinrich Rudolf Hertz]] (1857–1894), the first person to provide conclusive proof of the existence of [[electromagnetic wave]]s. For high frequencies, the unit is commonly expressed in [[metric prefix|multiples]]: kilohertz (kHz), megahertz (MHz), gigahertz (GHz), terahertz (THz).

Some of the unit's most common uses are in the description of [[periodic waveform]]s and [[musical tone]]s, particularly those used in [[radio]]- and audio-related applications. It is also used to describe the [[clock speed]]s at which computers and other electronics are driven. The units are sometimes also used as a representation of the [[photon energy|energy of a photon]], via the [[Planck relation]] ''E''&nbsp;=&nbsp;''hν'', where ''E'' is the photon's energy, ''ν'' is its frequency, and ''h'' is the [[Planck constant]].

== Definition ==
The hertz is defined as one per second for periodic events. The [[International Committee for Weights and Measures]] defined the second as "the duration of {{val|9192631770}} periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the [[caesium]]-133 atom"<ref>{{Cite web |url=https://www.bipm.org/en/publications/si-brochure/ |title=SI Brochure: The International System of Units (SI) § 2.3.1 Base units |year=2019 |publisher=[[International Bureau of Weights and Measures|BIPM]] |page=130 |language=en-gb, fr |edition=9th |format=PDF |access-date=2 February 2021}}</ref><ref>{{Cite web |url=https://www.bipm.org/en/publications/si-brochure/ |title=SI Brochure: The International System of Units (SI) § Appendix 1. Decisions of the CGPM and the CIPM |year=2019 |publisher=[[International Bureau of Weights and Measures|BIPM]] |page=169 |language=en-gb, fr |edition=9th |format=PDF |access-date=2 February 2021}}</ref> and then adds: "It follows that the hyperfine splitting in the ground state of the caesium 133 atom is exactly {{val|9192631770|u=hertz}}, {{nowrap|1=''ν''<sub>hfs Cs</sub> = {{val|9192631770|u=Hz}}}}." The dimension of the unit hertz is 1/time (T<sup>−1</sup>). Expressed in base SI units, the unit is the reciprocal second (1/s).

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, {{val|e=3|u=Hz}}), MHz (megahertz, {{val|e=6|u=Hz}}), GHz (gigahertz, {{val|e=9|u=Hz}}) and THz (terahertz, {{val|e=12|u=Hz}}). One hertz (i.e. one per second) simply means "one periodic event occurs per second" (where the event being counted may be a complete cycle); {{val|100|u=Hz}} means "one hundred periodic events occur per second", and so on. The unit may be applied to any periodic event—for example, a clock might be said to tick at {{val|1|u=Hz}}, or a human heart might be said to [[heart rate|beat]] at {{val|1.2|u=Hz}}.

The occurrence [[aperiodic frequency|rate of aperiodic]] or [[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 [[radioactivity]], in [[becquerel]]s.{{efn|"(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."<ref name="BIPMtable3">{{cite web |url=http://www.bipm.org/en/publications/si-brochure/section2-2.html#section2-2-2 |title=BIPM – Table 3 |publisher=[[BIPM]] | access-date=2012-10-24}}</ref>}} Whereas {{val|1|u=Hz}} (one per second) specifically refers to one cycle (or periodic event) per second, {{val|1|u=Bq}} (also one per second) specifically refers to one radionuclide event per second on average.

Even though frequency, [[angular velocity]], [[angular frequency]] and radioactivity all have the dimension T<sup>−1</sup>, of these only frequency is expressed using the unit 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 |archive-url=https://web.archive.org/web/20091001192328/http://www.bipm.org/en/si/derived_units/2-2-2.html |archive-date=1 October 2009}}</ref> Thus a disc rotating at 60 revolutions per minute (rpm) is said to have an angular velocity of 2{{pi}}&nbsp;rad/s and a [[rotational frequency|frequency of rotation]] of {{val|1|u=Hz}}. The correspondence between a frequency ''f'' with the unit hertz and an angular velocity ''ω'' with the unit [[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}}
{{Clear}}

==History==
{{further|Cycle per second}}

The hertz is named after the German physicist [[Heinrich Hertz]] (1857–1894), who made important scientific contributions to the study of [[electromagnetism]]. The name was established by the [[International Electrotechnical Commission]] (IEC) in 1935.<ref>{{cite web |url=http://www.iec.ch/about/history/overview/ |title=IEC History |publisher=Iec.ch |access-date=2021-01-06 |archive-date=19 May 2013 |archive-url=https://web.archive.org/web/20130519144600/http://www.iec.ch/about/history/overview/ |url-status=dead }}</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, "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.<ref>{{cite magazine
|last=Cartwright |first=Rufus |date=March 1967 |title=Will Success Spoil Heinrich Hertz? |url=https://www.worldradiohistory.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>{{Failed verification|date=June 2022|reason=The 1967 citation obviously doesn't say what happened in the 1970s.}}

In some usage, the "per second" was omitted, so that "megacycles" (Mc) was used as an abbreviation of "megacycles per second" (that is, megahertz (MHz)).<ref>{{cite journal | title = Ultrasonic Propagation in Liquids: I. Application of Pulse Technique to Velocity and Absorption Measurements at 15 Megacycles| year = 1946| last1 = Pellam| first1 = J. R.| last2 = Galt| first2 = J. K.| journal = The Journal of Chemical Physics| volume = 14| issue = 10| pages = 608–614| bibcode = 1946JChPh..14..608P| doi = 10.1063/1.1724072| hdl = 1721.1/5042| hdl-access = free}}</ref>

==Applications==
[[File:Wave frequency.gif|thumb|upright=1.8|A [[sine wave]] with varying frequency]]
[[File:Wiggers Diagram.svg|thumb|upright=1.8|[[Cardiac cycle|A heartbeat]] is an example of a non-[[Sine wave|sinusoidal]] periodic phenomenon that may be analyzed in terms of frequency. Two cycles are illustrated.]]

===Sound and vibration===
[[Sound]] is a traveling [[longitudinal wave]], which is an [[oscillation]] of [[pressure]]. Humans perceive the frequency of a sound as its [[Pitch (music)|pitch]]. Each [[musical note]] corresponds to a particular frequency. An infant's ear is able to perceive frequencies ranging from {{val|20|u=Hz}} to {{val|20000|u=Hz}}; the average [[Adult|adult human]] can hear sounds between {{val|20|u=Hz}} and {{val|16000|u=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 |access-date=2012-04-28 |url-status=dead |archive-url=https://web.archive.org/web/20120426090422/http://www.mmk.e-technik.tu-muenchen.de/persons/ter/top/dominant.html |archive-date=26 April 2012 |df=dmy-all }}</ref> The range of [[ultrasound]], [[infrasound]] and other physical vibrations such as [[molecular vibration|molecular]] and [[atom vibrations|atomic vibrations]] extends from a few [[femto]]hertz<ref name="science_nasa_gov">{{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|access-date=12 July 2017|archive-date=5 May 2021|archive-url=https://web.archive.org/web/20210505232620/https://science.nasa.gov/science-news/science-at-nasa/2003/09sep_blackholesounds/|url-status=dead}}</ref> into the [[tera-|tera]]hertz range{{efn|[[atom vibrations|Atomic vibrations]] are typically on the order of tens of terahertz}} and beyond.<ref name="science_nasa_gov" />

==={{anchor|Electricity}} Electromagnetic radiation===
[[Electromagnetic radiation]] is often described by its frequency—the number of oscillations 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), with the latter known as [[microwave]]s. [[Light]] is electromagnetic radiation that is even higher in frequency, and has frequencies in the range of tens of terahertz (THz, [[infrared]]) to a few petahertz (PHz, [[ultraviolet]]), with the [[visible spectrum]] being 400–790&nbsp;THz. 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 [[terahertz radiation]]. Even higher frequencies exist, such as that of [[X-ray]]s and [[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]]s or [[Photon energy|photon energies]]: for a more detailed treatment of this and the above frequency ranges, see ''[[Electromagnetic spectrum]]''.

=== Gravitational waves ===
Observations of [[gravitational wave]]s are conducted in the 30–7000&nbsp;Hz range by laser [[interferometer]]s like [[LIGO]], and the nanohertz (1–1000&nbsp;nHz) range by [[pulsar timing array]]s.  Future space-based detectors are planned to fill in the gap, with [[Laser Interferometer Space Antenna|LISA]] operating from 0.1–10&nbsp;mHz (with some sensitivity from 10&nbsp;μHz to 100&nbsp;mHz), and [[Deci-hertz Interferometer Gravitational wave Observatory|DECIGO]] in the 0.1–10&nbsp;Hz range.

===Computers===
{{further|topic=why frequency is a flawed speed indicator for computers|Megahertz myth}}
In computers, most [[central processing unit]]s (CPU) are labeled in terms of their [[clock rate]] expressed in megahertz ({{val|u=MHz}}) or gigahertz ({{val|u=GHz}}). This specification refers to the frequency of the CPU's master [[clock signal]]. This signal is nominally a [[Square wave (waveform)|square wave]], which is an electrical voltage that switches between low and high logic levels 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 [[Megahertz myth|easily manipulable benchmark]]. Some processors use multiple clock cycles 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 |access-date=2012-04-28}}</ref> For personal computers, CPU clock speeds have ranged from approximately {{val|1|u=MHz}} in the late 1970s ([[Atari]], [[Commodore International|Commodore]], [[Apple computers]]) to up to {{val|6|u=GHz}} in [[IBM Power microprocessors]].

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

== SI multiples ==
<!-- Other articles link here. -->
{{For|examples of various multiples|Orders of magnitude (frequency)}}
{{SI multiples
| symbol=Hz
| unit=hertz
| note=Common prefixed units are in bold.
| k= |M= |G= |T=
| 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 massive particles, although these are not directly observable and must be inferred through other phenomena. By convention, these are typically not expressed in hertz, but in terms of the equivalent energy, which is proportional to the frequency by the factor of the [[Planck constant]].

== Unicode==

The [[CJK Compatibility]] block in [[Unicode]] contains characters for common SI units for frequency. These are intended for compatibility with East Asian character encodings, and not for use in new documents (which would be expected to use Latin letters, e.g. "MHz").<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 |author-link=Unicode Consortium |date=2019 |website=Unicode.org}}</ref>

* {{unichar|3339}} ({{lang|ja|ヘルツ}}, {{Transliteration|ja|herutsu}})
* {{unichar|3390|Square Hz}} (Hz)
* {{unichar|3391|Square kHz}} (kHz)
* {{unichar|3392|Square MHz}} (MHz)
* {{unichar|3393|Square GHz}} (GHz)
* {{unichar|3394|Square THz}} (THz)

== See also ==
* [[Alternating current]]
* [[Bandwidth (signal processing)]]
* [[Electronic tuner]]
* [[FLOPS]]
* [[Frequency changer]]
* [[Normalized frequency (signal processing)]]
* [[Orders of magnitude (frequency)]]
* [[Orders of magnitude (rotational speed)]]
* [[Periodic function]]
* [[Radian per second]]
* [[Rate (mathematics)|Rate]]
* [[Sampling rate]]

== Notes ==
{{Notelist}}

== 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''] {{Webarchive|url=https://web.archive.org/web/20211205032940/https://nrc.canada.ca/en/stories/accuracy-single-ion-clock-pushed-new-limits |date=5 December 2021 }}
* [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''] (archived 23 December 2013)
* [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''] (archived 27 June 2013)
* [https://www.npl.co.uk/time-frequency/optical-atomic-clocks National Physical Laboratory: ''Time and frequency Optical atomic clocks'']

{{SI units}}

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