TheInfoList

Frequency is the number of occurrences of a repeating event per
unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparently irreversible process, irreversible succession from the past, through the presen ...
. It is also occasionally referred to as temporal frequency to emphasize the contrast to
spatial frequency In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...
, and ordinary frequency to emphasize the contrast to
angular frequency In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succ ...
. Frequency is measured in
hertz The hertz (symbol: Hz) is the unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in a theatric ...
(Hz) which is equal to one (event) per second. The period is the duration of time of one cycle in a repeating event, so the period is the
reciprocal Reciprocal may refer to: In mathematics * Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal'' * Reciprocal polynomial, a polynomial obtained from another poly ...

of the frequency. For example, if a heart beats at a frequency of 120 times a minute (2 hertz), its period, —the time interval between beats—is half a second (60 seconds divided by 120
beat Beat, beats or beating may refer to: Common meanings Assigned activity or area * Patrol, an area (usually geographic) that one is responsible to monitor, including: ** Beat (police), the territory and time that a police officer patrols ** Beat ...
s). Frequency is an important parameter used in science and engineering to specify the rate of and phenomena, such as mechanical vibrations,
audio signal An audio signal is a representation of sound, typically using either a changing level of electrical voltage for analog signals, or a series of binary numbers for Digital signal (signal processing), digital signals. Audio signals have frequencies i ...
s (
sound In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...

),
radio wave Radio waves are a type of electromagnetic radiation In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies ma ...
s, and
light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that can be visual perception, perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 ...

.

# Definitions and units

For cyclical phenomena such as
oscillation Oscillation is the repetitive variation, typically in time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparently irreversible process, irreversible succession from the pas ...

s,
wave In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ...

s, or for examples of
simple harmonic motion In mechanics and physics, simple harmonic motion (sometimes abbreviated ) is a special type of Periodic function, periodic motion where the restoring force on the moving object is directly Proportionality (mathematics), proportional to the magni ...

, the term ''frequency'' is defined as the number of cycles or vibrations per unit of time. The conventional symbol for frequency is ''f''; the Greek letter ''$\nu$'' ( nu) is also used. The ''period'' $T$ is the time taken to complete one cycle of an oscillation. The relation between the frequency and the period is given by the equation: :$f = \frac.$ The term ''temporal frequency'' is used to emphasise that the frequency is characterised by the number of occurrences of a repeating event per unit time, and not unit distance. The
SI derived unit SI derived units are units of measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, which can be used to compare with other objects o ...
of frequency is the
hertz The hertz (symbol: Hz) is the unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in a theatric ...

(Hz), named after the German physicist
Heinrich Hertz Heinrich Rudolf Hertz ( ; ; 22 February 1857 – 1 January 1894) was a German who first conclusively proved the existence of the predicted by 's . The unit of frequency, , was named the "" in his honor.
by the
International Electrotechnical Commission The International Electrotechnical Commission (IEC; in French French (french: français(e), link=no) may refer to: * Something of, from, or related to France France (), officially the French Republic (french: link=no, République franç ...
in 1930. It was adopted by the
CGPM 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 The International Bureau of Weights and Measures (f ...
(Conférence générale des poids et mesures) in 1960, officially replacing the previous name, "
cycles per second The cycle per second was a once-common English name for the unit of frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial ...
" (cps). The unit for the period, as for all measurements of time, is the
second The second (symbol: s, also abbreviated: sec) is the of in the (SI) (french: Système International d’unités), commonly understood and historically defined as of a – this factor derived from the division of the day first into 24 s, th ...
. A traditional unit of measure used with rotating mechanical devices is
revolutions per minute Revolutions per minute (abbreviated rpm, RPM, rev/min, r/min, or with the notation min−1) is the number of turns in one minute The minute is a unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the ...
, abbreviated r/min or rpm. 60 rpm is equivalent to one hertz. Wind-generated waves are described in terms of their period rather than frequency.

# Period versus frequency

As a matter of convenience, longer and slower waves, such as
ocean surface wave In , a wind wave, or wind-generated wave, is a water that occurs on the of . Wind waves result from the blowing over a fluid surface, where the contact distance in the direction of the wind is known as the '. Waves in the oceans can travel ...

s, tend to be described by wave period rather than frequency. Short and fast waves, like
audio Audio most commonly refers to sound In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion ( ...

and radio, are usually described by their frequency instead of period. Some commonly used conversions are listed below:

# Related types of frequency

*
Angular frequency In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succ ...
, usually denoted by the Greek letter ''ω'' (omega), is defined as the rate of change of
angular displacement Angular displacement of a body is the angle In Euclidean geometry, an angle is the figure formed by two Ray (geometry), rays, called the ''sides'' of the angle, sharing a common endpoint, called the ''vertex (geometry), vertex'' of the angle. ...
(during rotation), , or the rate of change of the
phase Phase or phases may refer to: Science * State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter) In the physical sciences, a phase is a region of space (a thermodynamic system A thermodynamic system is a ...
of a
sinusoid A sine wave or sinusoid is a mathematical curve that describes a smooth periodic oscillation. A sine wave is a continuous wave. It is named after the function sine, of which it is the graph. It occurs often in both pure and applied mathemat ...

al waveform (notably in oscillations and waves), or as the rate of change of the
argument In logic Logic is an interdisciplinary field which studies truth and reasoning Reason is the capacity of consciously making sense of things, applying logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, lab ...
to the
sine function In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is oppo ...

: $y(t) = \sin\left( \theta(t) \right) = \sin(\omega t) = \sin(2 \mathrm f t)$ $\frac = \omega = 2 \mathrm f$ Angular frequency is commonly measured in
radian The radian, denoted by the symbol \text, is the SI unit for measuring angle In Euclidean geometry, an angle is the figure formed by two Ray (geometry), rays, called the ''sides'' of the angle, sharing a common endpoint, called the ''verte ...

s per second (rad/s) but, for
discrete-time signalIn mathematical dynamics, discrete time and continuous time are two alternative frameworks within which to model variables that evolve over time. Discrete time Discrete sampled signal Discrete time views values of variables as occurring at disti ...
s, can also be expressed as radians per sampling interval, which is a
dimensionless quantity In dimensional analysis, a dimensionless quantity is a quantity to which no physical dimension is assigned, also known as a bare, pure, or scalar quantity or a quantity of dimension one, with a corresponding unit of measurement in the International ...
. Angular frequency (in rad/s) is larger than ordinary frequency (in Hz) by a factor of 2π. *
Spatial frequency In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...
is analogous to temporal frequency, but the time axis is replaced by one or more spatial displacement axes, e.g.: $y(t) = \sin\left( \theta(t,x) \right) = \sin(\omega t + kx)$ $\frac = k$
Wavenumber In the physical science Physical science is a branch of natural science that studies non-living systems, in contrast to life science. It in turn has many branches, each referred to as a "physical science", together called the "physical scienc ...
, ''k'', is the spatial frequency analogue of angular temporal frequency and is measured in radians per
metre The metre ( Commonwealth spelling) or meter (American spelling Despite the various English dialects spoken from country to country and within different regions of the same country, there are only slight regional variations in English o ...
. In the case of more than one spatial dimension, wavenumber is a
vector Vector may refer to: Biology *Vector (epidemiology) In epidemiology Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and risk factor, determinants of health and disease conditions in defined pop ...
quantity.

# In wave propagation

For periodic waves in (that is, media in which the wave speed is independent of frequency), frequency has an inverse relationship to the
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 (waves), phase on the wave, such as two adja ...

, ''λ'' (
lambda Lambda (; uppercase , lowercase ; el, λάμ(β)δα, ''lám(b)da'') is the 11th letter of the Greek alphabet, representing the sound Dental, alveolar and postalveolar lateral approximants, /l/. In the system of Greek numerals, lambda has a v ...

). Even in dispersive media, the frequency ''f'' of a sinusoidal wave is equal to the
phase velocity in groups of gravity wave , Croatia in July 2009. Image:wave clouds.jpg, Wave clouds over Theresa, Wisconsin, United States in August 2005. In fluid dynamics, gravity waves are waves generated in a fluid medium or at the interface (matter), inter ...

''v'' of the wave divided by the wavelength ''λ'' of the wave: :$f = \frac.$ In the
special case In logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=none, lit=possessed of reason, intellectual, dialectical, argumentative, translit=logikḗ)Also related to (''logos''), "word, thought, idea, argument, a ...
of electromagnetic waves moving through a
vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameter A parameter (from the Ancient Gree ...

, then ''v = c'', where ''c'' is the
speed of light The speed of light in vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "Void (astronomy), void". An approximation to such vacuum is a region with a gaseous pressure m ...
in a vacuum, and this expression becomes: :$f = \frac.$ When monochromatic waves travel from one
medium Medium may refer to: Science and technology Aviation *Medium bomber, a class of war plane *Tecma Medium, a French hang glider design Communication * Media (communication), tools used to store and deliver information or data * Medium of i ...
to another, their frequency remains the same—only their wavelength and
speed In everyday use and in kinematics Kinematics is a subfield of physics, developed in classical mechanics, that describes the Motion (physics), motion of points, bodies (objects), and systems of bodies (groups of objects) without considerin ...
change.

# Measurement

Measurement of frequency can be done in the following ways:

## Counting

Calculating the frequency of a repeating event is accomplished by counting the number of times that event occurs within a specific time period, then dividing the count by the length of the time period. For example, if 71 events occur within 15 seconds the frequency is: :$f = \frac \approx 4.73 \, \text$ If the number of counts is not very large, it is more accurate to measure the time interval for a predetermined number of occurrences, rather than the number of occurrences within a specified time. The latter method introduces a
random error Observational error (or measurement error) is the difference between a measured value of a quantity and its true value.Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. In statistics Statistics is the discipline that co ...
into the count of between zero and one count, so on
average In colloquial language, an average is a single number taken as representative of a non-empty list of numbers. Different concepts of average are used in different contexts. Often "average" refers to the arithmetic mean, the sum of the numbers divide ...

half a count. This is called ''gating error'' and causes an average error in the calculated frequency of $\Delta f = \frac$, or a fractional error of $\frac = \frac$ where $T$ is the timing interval and $f$ is the measured frequency. This error decreases with frequency, so it is generally a problem at low frequencies where the number of counts ''N'' is small.

## Stroboscope

An old method of measuring the frequency of rotating or vibrating objects is to use a
stroboscope A stroboscope, also known as a strobe, is an instrument used to make a cyclically moving object appear to be slow-moving, or stationary. It consists of either a rotating disk with slots or holes or a lamp such as a flashtube which produces br ...
. This is an intense repetitively flashing light (
strobe light A strobe light or stroboscopic lamp, commonly called a strobe, is a device used to produce regular flashes of light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that can be visual ...
) whose frequency can be adjusted with a calibrated timing circuit. The strobe light is pointed at the rotating object and the frequency adjusted up and down. When the frequency of the strobe equals the frequency of the rotating or vibrating object, the object completes one cycle of oscillation and returns to its original position between the flashes of light, so when illuminated by the strobe the object appears stationary. Then the frequency can be read from the calibrated readout on the stroboscope. A downside of this method is that an object rotating at an integer multiple of the strobing frequency will also appear stationary.

## Frequency counter

Higher frequencies are usually measured with a
frequency counter A frequency counter is an electronics, electronic measuring instrument, instrument, or Electronic component, component of one, that is used for measuring frequency. Frequency counters usually measure the number of cycles of oscillation, or pulses p ...

. This is an
electronic instrument An electronic musical instrument or electrophone is a musical instrument A musical instrument is a device created or adapted to make musical sounds. In principle, any object that produces sound can be considered a musical instrument—it is th ...
which measures the frequency of an applied repetitive electronic
signal In signal processing Signal processing is an electrical engineering subfield that focuses on analysing, modifying, and synthesizing signals such as audio signal processing, sound, image processing, images, and scientific measurements. Sig ...
and displays the result in hertz on a
digital display s, LED An LED A light-emitting diode (LED) is a semiconductor A semiconductor material has an Electrical resistivity and conductivity, electrical conductivity value falling between that of a Electrical conductor, conductor, such as me ...
. It uses
digital logic A logic gate is an idealized model of computation In computer science Computer science deals with the theoretical foundations of information, algorithms and the architectures of its computation as well as practical techniques for their app ...
to count the number of cycles during a time interval established by a precision
quartz Quartz is a hard, crystalline mineral composed of silica (silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon-oxygen Tetrahedral molecular geometry, tetrahedra, with each oxygen being shared between two tetrahedra, ...

time base. Cyclic processes that are not electrical, such as the rotation rate of a shaft, mechanical vibrations, or
sound wave In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...

s, can be converted to a repetitive electronic signal by
transducer A transducer is a device that converts Religious conversion is the adoption of a set of beliefs identified with one particular religious denomination A religious denomination is a subgroup within a religion Religion is a social system ...

s and the signal applied to a frequency counter. As of 2018, frequency counters can cover the range up to about 100 GHz. This represents the limit of direct counting methods; frequencies above this must be measured by indirect methods.

## Heterodyne methods

Above the range of frequency counters, frequencies of electromagnetic signals are often measured indirectly utilizing
heterodyning A heterodyne is a signal frequency that is created by combining or mixing two other frequencies using a signal processing technique called ''heterodyning'', which was invented by Canadian inventor-engineer Reginald Fessenden. Heterodyning is use ...
( frequency conversion). A reference signal of a known frequency near the unknown frequency is mixed with the unknown frequency in a nonlinear mixing device such as a
diode A diode is a two- that conducts primarily in one direction (asymmetric ); it has low (ideally zero) in one direction, and high (ideally infinite) in the other. A diode or thermionic diode is a vacuum tube with two s, a heated and a , in ...

. This creates a
heterodyne A heterodyne is a signal frequency that is created by combining or mixing two other frequencies using a signal processing technique called ''heterodyning'', which was invented by Canadian inventor-engineer Reginald Fessenden. Heterodyning is use ...

or "beat" signal at the difference between the two frequencies. If the two signals are close together in frequency the heterodyne is low enough to be measured by a frequency counter. This process only measures the difference between the unknown frequency and the reference frequency. To reach higher frequencies, several stages of heterodyning can be used. Current research is extending this method to infrared and light frequencies ( optical heterodyne detection).

# Examples

## Light

Visible light is an
electromagnetic wave In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...

, consisting of oscillating
electric Electricity is the set of physics, physical Phenomenon, phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnet ...

and
magnetic field A magnetic field is a vector field In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space. For instance, a vector field in the plane can be visualised as a collection of arrows with ...

s traveling through space. The frequency of the wave determines its color: 400 THz ( Hz) is red light, 800 THz () is violet light, and between these (in the range 400–800 THz) are all the other colors of the
visible spectrum The visible spectrum is the portion of the that is to the . in this range of s is called ' or simply . A typical will respond to wavelengths from about 380 to about 750 . In terms of frequency, this corresponds to a band in the vicinity of ...
. An electromagnetic wave with a frequency less than will be invisible to the human eye; such waves are called
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of Light, visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from ...

(IR) radiation. At even lower frequency, the wave is called a
microwave Microwave is a form of electromagnetic radiation In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies mat ...

, and at still lower frequencies it is called a
radio wave Radio waves are a type of electromagnetic radiation In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies ma ...
. Likewise, an electromagnetic wave with a frequency higher than will also be invisible to the human eye; such waves are called
ultraviolet Ultraviolet (UV) is a form of electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, ...

(UV) radiation. Even higher-frequency waves are called
X-ray An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Moti ...

s, and higher still are
gamma ray A gamma ray, also known as gamma radiation (symbol γ or \gamma), is a penetrating form of electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, it ...
s. All of these waves, from the lowest-frequency radio waves to the highest-frequency gamma rays, are fundamentally the same, and they are all called
electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...

. They all travel through a vacuum at the same speed (the speed of light), giving them wavelengths inversely proportional to their frequencies. :$\displaystyle c=f\lambda$ where ''c'' is the speed of light (''c'' in a vacuum or less in other media), ''f'' is the frequency and λ is the wavelength. In dispersive media, such as glass, the speed depends somewhat on frequency, so the wavelength is not quite inversely proportional to frequency.

## Sound

Sound propagates as mechanical vibration waves of pressure and displacement, in air or other substances. In general, frequency components of a sound determine its "color", its
timbre In music, timbre ( ), also known as tone color or tone quality (from ), is the perceived sound quality of a , sound or . Timbre distinguishes different types of sound production, such as choir voices and musical instruments. It also enables li ...

. When speaking about the frequency (in singular) of a sound, it means the property that most determines its
pitch Pitch may refer to: Acoustic frequency * Pitch (music), the perceived frequency of sound including "definite pitch" and "indefinite pitch" ** Absolute pitch or "perfect pitch" ** Pitch class, a set of all pitches that are a whole number of octaves ...
. The frequencies an ear can hear are limited to a specific range of frequencies. The
audible frequency An audio frequency or audible frequency (AF) is a periodic vibration Vibration is a mechanical phenomenon whereby oscillation Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point ...
range for humans is typically given as being between about 20 Hz and 20,000 Hz (20 kHz), though the high frequency limit usually reduces with age. Other
species In biology, a species is the basic unit of biological classification, classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined as the largest group of organisms in which any two individu ...

have different hearing ranges. For example, some dog breeds can perceive vibrations up to 60,000 Hz. In many media, such as air, the
speed of sound The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elasticity (solid mechanics), elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends s ...
is approximately independent of frequency, so the wavelength of the sound waves (distance between repetitions) is approximately inversely proportional to frequency.

## Line current

In
Europe Europe is a continent A continent is any of several large landmass A landmass, or land mass, is a large region In geography Geography (from Greek: , ''geographia'', literally "earth description") is a field of scienc ...

,
Africa Africa is the world's second-largest and second-most populous continent A continent is any of several large landmass A landmass, or land mass, is a large region In geography Geography (from Greek: , ''geographia'', ...

,
Australia Australia, officially the Commonwealth of Australia, is a Sovereign state, sovereign country comprising the mainland of the Australia (continent), Australian continent, the island of Tasmania, and numerous List of islands of Australia, sma ...

, southern
South America South America is a continent A continent is any of several large landmasses. Generally identified by convention (norm), convention rather than any strict criteria, up to seven geographical regions are commonly regarded as continent ...

, most of
Asia Asia () is Earth's largest and most populous continent, located primarily in the Eastern Hemisphere, Eastern and Northern Hemisphere, Northern Hemisphere of the Earth, Hemispheres. It shares the continental landmass of Eurasia with the cont ...

, and
Russia Russia ( rus, link=no, Россия, Rossiya, ), or the Russian Federation, is a country spanning Eastern Europe Eastern Europe is the eastern region of . There is no consistent definition of the precise area it covers, partly because th ...

, the frequency of the
alternating current Alternating current (AC) is an electric current An electric current is a stream of charged particle In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'natu ...
in household electrical outlets is 50 Hz (close to the
tone Tone may refer to: Color-related * Tone, mix of tint and shade, in painting and color theory * Tone, the lightness Lightness is a visual perception of the luminance (L) of an object. It is often judged relative to a similarly lit object. ...
G), whereas in
North America North America is a continent A continent is any of several large landmasses. Generally identified by convention (norm), convention rather than any strict criteria, up to seven geographical regions are commonly regarded as continen ...

and northern South America, the frequency of the alternating current in household electrical outlets is 60 Hz (between the tones B♭ and B; that is, a
minor third In music theory, a minor third is a interval (music), musical interval that encompasses three half steps, or semitones. Staff notation represents the minor third as encompassing three staff positions (see: interval (music)#Number, interval numbe ...
above the European frequency). The frequency of the ' hum' in an
audio recording Sound recording and reproduction is an electrical Electricity is the set of physical phenomena associated with the presence and motion Image:Leaving Yongsan Station.jpg, 300px, Motion involves a change in position In physics, motion ...
can show where the recording was made, in countries using a European, or an American, grid frequency.

# Aperiodic frequency

Aperiodic frequency is the rate of incidence or occurrence of non-
cyclic Cycle or cyclic may refer to: Anthropology and social sciences * Cyclic history, a theory of history * Cyclical theory, a theory of American political history associated with Arthur Schlesinger, Sr. * Social cycle, various cycles in social scienc ...

phenomena, including random processes such as
radioactive decay Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is conside ...

. It is expressed in
units of measurement A unit of measurement is a definite magnitude Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude (mathematics), the relative size of an object *Norm (mathematic ...
of reciprocal seconds (s−1) or, in the case of radioactivity,
becquerels The becquerel (; symbol: Bq) is the SI derived unit SI derived units are units of measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or eve ...
.
Bureau international des poids et mesures The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation An intergovernmental organization (IGO) is an organization composed primarily of sovereign states ...

''Le Système international d’unités (SI) / The International System of Units (SI)'', 9th ed.
(Sèvres: 2019), ISBN 978‑92‑822‑2272‑0, sub§2.3.4, Table 4.
It is defined as a
ratio In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8∶6, which is equivalent to ...

, ''f'' = ''N''/''T'', involving the number of times an
event Event may refer to: Gatherings of people * Ceremony A ceremony (, ) is a unified ritual A ritual is a sequence of activities involving gestures, words, actions, or objects, performed in a sequestered place and according to a set sequence. Rit ...
happened (''N'') during a given time
duration Duration may refer to: * The amount of Time#Terminology, time elapsed between two events * Duration (music) – an amount of time or a particular time interval, often cited as one of the fundamental aspects of music * Duration (philosophy) – a th ...

(''T''); it is a
physical quantity A physical quantity is a physical property of a material or system that can be Quantification (science), quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a ''numerical value'' ...
of type temporal rate.

*
Audio frequency An audio frequency or audible frequency (AF) is a periodic vibration Vibration is a mechanical phenomenon whereby oscillation Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point o ...
*
Bandwidth (signal processing) Bandwidth is the difference between the upper and lower frequencies Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progr ...
*
Cutoff frequency In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force ...
*
DownsamplingIn digital signal processing, downsampling, compression, and decimation are terms associated with the process of sample rate conversion, ''resampling'' in a multi-rate digital signal processing system. Both ''downsampling'' and ''decimation'' can be ...
*
Electronic filter Electronic filters are a type of signal processing filter in the form of electrical circuits. This article covers those filters consisting of lumped electronic components, as opposed to distributed-element filter A distributed-element filte ...
*
Fourier analysis In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis ...
*
Frequency band A frequency band is an interval in the frequency domain, delimited by a lower frequency and an upper frequency. The term may refer to a radio band or an interval of some other spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a c ...
*
Frequency converter A frequency changer or frequency converter is an Electronics, electronic or electromechanical device that converts alternating current (Alternating current, AC) of one frequency to alternating current of another frequency. The device may also chan ...

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Frequency domain In physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or Signal (information theory), signals with respect to frequency, rather than time. Put simply, a time-dom ...
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Frequency distributionIn statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a ...

* Frequency extender *
Frequency grid{{Context, date=October 2009 A frequency grid is a table of all the central frequency, frequencies (and corresponding wavelengths) of channels allowed in a communications system. The most common frequency grid used for fiber-optic communication is ...
*Frequency modulation *Frequency spectrum *Interaction frequency *Least-squares spectral analysis *Natural frequency *Negative frequency *Periodicity (disambiguation) *Pink noise *Preselector *Radar signal characteristics *Signaling (telecommunications) *Spread spectrum *Spectral component *Transverter *Upsampling *Orders of magnitude (frequency)

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