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The hertz (symbol: Hz) is the unit of
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is e ...
in the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...
(SI), equivalent to one event (or cycle) per
second The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds e ...
. The hertz is an
SI derived unit SI derived units are units of measurement derived from the seven base units specified by the International System of Units (SI). They can be expressed as a product (or ratio) of one or more of the base units, possibly scaled by an appropriate ...
whose expression in terms of
SI base unit The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which al ...
s is s−1, meaning that one hertz is the reciprocal of one second. It is named after Heinrich Rudolf Hertz (1857–1894), the first person to provide conclusive proof of the existence of
electromagnetic wave In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) ligh ...
s. Hertz are commonly expressed in multiples: kilohertz (kHz), megahertz (MHz), gigahertz (GHz), terahertz (THz). Some of the unit's most common uses are in the description of periodic waveforms and musical tones, particularly those used in
radio Radio is the technology of signaling and communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300  gigahertz (GHz). They are generated by an electronic device called a trans ...
- and audio-related applications. It is also used to describe the
clock speed In computing, the clock rate or clock speed typically refers to the frequency at which the clock generator of a processor can generate pulses, which are used to synchronize the operations of its components, and is used as an indicator of the p ...
s at which computers and other electronics are driven. The units are sometimes also used as a representation of the energy of a photon, via the Planck relation ''E'' = ''hν'', where ''E'' is the photon's energy, ''ν'' is its frequency, and ''h'' is the
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivale ...
.

# Definition

The hertz is equivalent to one
cycle per second The cycle per second is a once-common English name for the unit of frequency now known as the hertz (Hz). The plural form was typically used, often written cycles per second, cycles/second, c.p.s., c/s, or, ambiguously, just cycles (Cy./Cyc.). The ...
. The
International Committee for Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence générale des poids et mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established i ...
defined the second as "the duration of periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the
caesium Caesium (IUPAC spelling) (or cesium in American English) is a chemical element with the symbol Cs and atomic number 55. It is a soft, silvery-golden alkali metal with a melting point of , which makes it one of only five elemental metals that ...
-133 atom" and then adds: "It follows that the hyperfine splitting in the ground state of the caesium 133 atom is exactly , ." The dimension of the unit hertz is 1/time (T−1). Expressed in base SI units, the unit is the reciprocal second (1/s). In English, "hertz" is also used as the plural form. As an SI unit, Hz can be prefixed; commonly used multiples are kHz (kilohertz, ), MHz (megahertz, ), GHz (gigahertz, ) and THz (terahertz, ). One hertz simply means "one event per second" (where the event being counted may be a complete cycle); means "one hundred events per second", and so on. The unit may be applied to any periodic event—for example, a clock might be said to tick at , or a human heart might be said to
beat Beat, beats or beating may refer to: Common uses * Patrol, or beat, a group of personnel assigned to monitor a specific area ** Beat (police), the territory that a police officer patrols ** Gay beat, an area frequented by gay men * Battery (c ...
at . The occurrence rate of aperiodic or
stochastic Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselve ...
events is expressed in reciprocal second or inverse second (1/s or s−1) in general or, in the specific case of radioactivity, in becquerels."(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." Whereas is one cycle (or periodic event) per second, is one radionuclide event per second on average. Even though frequency,
angular velocity In physics, angular velocity or rotational velocity ( or ), also known as angular frequency vector,(UP1) is a pseudovector representation of how fast the angular position or orientation of an object changes with time (i.e. how quickly an objec ...
,
angular frequency In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit ti ...
and radioactivity all have the dimension T−1, of these only frequency is expressed using the unit hertz. Thus a disc rotating at 60 revolutions per minute (rpm) is said to have an angular velocity of 2 rad/s and a frequency of rotation of . The correspondence between a frequency ''f'' with the unit hertz and an angular velocity ''ω'' with the unit radians per second is :$\omega = 2\pi f$ and $f = \frac .$

# History

The hertz is named after the German physicist
Heinrich Hertz Heinrich Rudolf Hertz ( ; ; 22 February 1857 – 1 January 1894) was a German physicist who first conclusively proved the existence of the electromagnetic waves predicted by James Clerk Maxwell's equations of electromagnetism. The unit o ...
(1857–1894), who made important scientific contributions to the study of
electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of ...
. The name was established by the
International Electrotechnical Commission The International Electrotechnical Commission (IEC; in French: ''Commission électrotechnique internationale'') is an international standards organization that prepares and publishes international standards for all electrical, electronic and ...
(IEC) in 1935. It was adopted by the
General Conference on Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence générale des poids et mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established i ...
(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. 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)).

# Applications

## Sound and vibration

Sound In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by ...
is a traveling
longitudinal wave Longitudinal waves are waves in which the vibration of the medium is parallel ("along") to the direction the wave travels and displacement of the medium is in the same (or opposite) direction of the wave propagation. Mechanical longitudinal w ...
, which is an oscillation of
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and ...
. Humans perceive the frequency of a sound as its pitch. Each
musical note In music, a note is the representation of a musical sound. Notes can represent the pitch and duration of a sound in musical notation. A note can also represent a pitch class. Notes are the building blocks of much written music: discretizatio ...
corresponds to a particular frequency. An infant's ear is able to perceive frequencies ranging from to ; the average adult human can hear sounds between and . The range of
ultrasound Ultrasound is sound waves with frequencies higher than the upper audible limit of human hearing. Ultrasound is not different from "normal" (audible) sound in its physical properties, except that humans cannot hear it. This limit varies ...
, infrasound and other physical vibrations such as molecular and atomic vibrations extends from a few
femto A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The pre ...
hertz into the terahertz range and beyond.

Electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) l ...
is often described by its frequency—the number of
oscillation Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulu ...
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).
Light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 t ...
is electromagnetic radiation that is even higher in frequency, and has frequencies in the range of tens (
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from arou ...
) to thousands (
ultraviolet Ultraviolet (UV) is a form of electromagnetic radiation with wavelength from 10 nm (with a corresponding frequency around 30  PHz) to 400 nm (750  THz), shorter than that of visible light, but longer than X-rays. UV radiatio ...
) 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
terahertz radiation Terahertz radiation – also known as submillimeter radiation, terahertz waves, tremendously high frequency (THF), T-rays, T-waves, T-light, T-lux or THz – consists of electromagnetic waves within the ITU-designated band of frequ ...
. Even higher frequencies exist, such as that of
gamma ray A gamma ray, also known as gamma radiation (symbol γ or \gamma), is a penetrating form of electromagnetic radiation arising from the radioactive decay of atomic nuclei. It consists of the shortest wavelength electromagnetic waves, typically ...
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 In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tr ...
s or
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are Massless particle, massless ...
energies: for a more detailed treatment of this and the above frequency ranges, see ''
Electromagnetic spectrum The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies. The electromagnetic spectrum covers electromagnetic waves with frequencies ranging fro ...
''.)

## Computers

In computers, most
central processing unit A central processing unit (CPU), also called a central processor, main processor or just processor, is the electronic circuitry that executes instructions comprising a computer program. The CPU performs basic arithmetic, logic, controlling, ...
s (CPU) are labeled in terms of their
clock rate In computing, the clock rate or clock speed typically refers to the frequency at which the clock generator of a processor can generate pulses, which are used to synchronize the operations of its components, and is used as an indicator of the ...
expressed in megahertz () or gigahertz (). This specification refers to the frequency of the CPU's master
clock signal In electronics and especially synchronous digital circuits, a clock signal (historically also known as ''logic beat'') oscillates between a high and a low state and is used like a metronome to coordinate actions of digital circuits. A clock sig ...
. This signal is nominally a
square wave A square wave is a non-sinusoidal periodic waveform in which the amplitude alternates at a steady frequency between fixed minimum and maximum values, with the same duration at minimum and maximum. In an ideal square wave, the transitions b ...
, 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 easily manipulable benchmark. Some processors use multiple clock cycles to perform a single operation, while others can perform multiple operations in a single cycle. For personal computers, CPU clock speeds have ranged from approximately in the late 1970s (
Atari Atari () is a brand name that has been owned by several entities since its inception in 1972. It is currently owned by French publisher Atari SA through a subsidiary named Atari Interactive. The original Atari, Inc., founded in Sunnyvale, Calif ...
, Commodore, Apple computers) to up to in
IBM Power microprocessors IBM Power microprocessors (originally POWER prior to Power10) are designed and sold by IBM for servers and supercomputers. The name "POWER" was originally presented as an acronym for "Performance Optimization With Enhanced RISC". The Power l ...
. Various
computer buses In computer architecture, a bus (shortened form of the Latin '' omnibus'', and historically also called data highway or databus) is a communication system that transfers data between components inside a computer, or between computers. This ...
, such as the
front-side bus A front-side bus (FSB) is a computer communication interface (bus) that was often used in Intel-chip-based computers during the 1990s and 2000s. The EV6 bus served the same function for competing AMD CPUs. Both typically carry data between the ...
connecting the CPU and northbridge, also operate at various frequencies in the megahertz range.

# SI multiples

Higher frequencies than the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...
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 The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivale ...
.

# Unicode

The CJK Compatibility block in
Unicode Unicode, formally The Unicode Standard,The formal version reference is is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, whi ...
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"). * * * * *

*
Alternating current Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in whic ...
*
Bandwidth (signal processing) Bandwidth is the difference between the upper and lower frequencies in a continuous band of frequencies. It is typically measured in hertz, and depending on context, may specifically refer to '' passband bandwidth'' or '' baseband bandwidth ...
* Electronic tuner * FLOPS * Frequency changer * Normalized frequency (signal processing) *
Orders of magnitude (frequency) The following list illustrates various frequencies, measured in hertz, according to decade A decade () is a period of ten years. Decades may describe any ten-year period, such as those of a person's life, or refer to specific groupings of cale ...
*
Periodic function A periodic function is a function that repeats its values at regular intervals. For example, the trigonometric functions, which repeat at intervals of 2\pi radians, are periodic functions. Periodic functions are used throughout science to de ...
*
Radian per second The radian per second (symbol: rad⋅s−1 or rad/s) is the unit of angular velocity in the International System of Units (SI). The radian per second is also the SI unit of angular frequency, commonly denoted by the Greek letter ''ω'' (omega) ...
* Rate *
Sampling rate In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave to a sequence of "samples". A sample is a value of the signal at a point in time and/or spa ...