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 Angular frequency omega, ''ω'' (in radians per second), is larger than frequency ''ν'' (in cycles per second, also called Hertz, Hz), by a factor of . This figure uses the symbol ''ν'', rather than ''f'' to denote frequency. In physics, angular ...
. 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 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 ( ...
s (
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 the br ...

),
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, of some measure about a central value (often a point of equilibrium) or between two or more different states. The term '' vibration'' is precisely used to describe mechanical oscillati ...

s,
wave In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through ...

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 or ...
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 physicist who first conclusively proved the existence of the electromagnetic waves predicted by James Clerk Maxwell's Maxwell's equations, equations of electroma ...

by the
International Electrotechnical Commission The International Electrotechnical Commission (IEC; in French language, French: ''Commission électrotechnique internationale'') is an international standards organization that prepares and publishes international standards for all electrical, el ...
in 1930. It was adopted by the
CGPM The General Conference on Weights and Measures ( French: ''Conférence Générale des Poids et Mesures'', abbreviated CGPM and sometimes referred to as the GCWM) is the supreme authority of the International Bureau of Weights and Measures, the in ...
(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 base unit of time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparently irreversible process, irreversible succession ...
. 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. It is a unit of rotational speed Rotational speed (or speed of revolution) of an object rotating around an ax ...
, 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 fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the study of air and other gas ...

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 Angular frequency omega, ''ω'' (in radians per second), is larger than frequency ''ν'' (in cycles per second, also called Hertz, Hz), by a factor of . This figure uses the symbol ''ν'', rather than ''f'' to denote frequency. In physics, angular ...
, 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 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). ...

: $y(t) = \sin\left( \theta(t) \right) = \sin(\omega t) = \sin(2 \mathrm f t)$ $\frac = \omega = 2 \mathrm f$ Angular frequency is commonly measured in
radian The radian, denoted by the symbol \text, is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as ...

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 sciences, the wavenumber (also wave number or repetency) is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance. Whereas temporal frequency can be thought of as the number of waves per ...
, ''k'', is the spatial frequency analogue of angular temporal frequency and is measured in radians per
metre The metre (British English, Commonwealth spelling) or meter (American English, American spelling; American and British English spelling differences#-re, -er, see spelling differences) (from the French unit , from the Greek noun , "measure", and ...
. 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 nondispersive media (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 adjac ...

, ''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 waves on the surface of deep water. The red square moves with the phase velocity, and the       green circles propagate with the group velocity. In this deep-water case, ''the phase velocity is twice ...

''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 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 much less than atmospheric pressure. Ph ...

, then ''v = c'', where ''c'' is the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant important in many areas of physics. Its exact value is defined as (approximately ). It is exact because, by international agreement, a Metre#Speed of light def ...
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, the speed (commonly referred to as ''v'') of an object is the magnitude (mathematics), magnitude of the rate of change of its Position (vector), position with time or the magnitude of the change of its posit ...
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, ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list (the arithmetic mean). For example, the average of the numbers 2 ...
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 electronic instrument Instrument may refer to: Science and technology * Flight instruments two-seat light airplane. The flight instruments are visible on the left of the instrument panel Flight instruments are the in ...

. This is an
electronic instrument An electronic musical instrument is a musical instrument that produces sound using electronics, electronic circuitry. Such an instrument sounds by outputting an electrical, electronic or digital audio signal that ultimately is plugged into a power ...
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 display and VF display, top to bottom. A display device is an output device for presentation of information in visual or Touch, tactile form (the latter used for example in Refreshable Braille display, tactile electronic displays for blin ...
. It uses
digital logic A logic gate is an idealized model of computation or physical electronic device implementing a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the te ...
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 (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior throug ...

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 Various semiconductor diodes. Bottom: A bridge rectifier. In most diodes, a white or black painted band identifies the cathode into which electrons will flow when the diode is conducting. Electron flow is the reverse of conventional current flow ...
. 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 Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is carried by electromagneti ...

, 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 that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the ...

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 File:Light Amplification by Stimulated Emission of Radiation.jpg, Laser beams with visible spectrum The visible spectrum is the portion of the electromagnetic spectrum that is visual perception, visible to the human eye. Electromagnetic radiation ...
. 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 visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from the n ...

(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 (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that stud ...

(UV) radiation. Even higher-frequency waves are called
X-ray An X-ray, or X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 Picometer, picometers to 10 Nanometer, nanometers, corresponding to frequency, frequencies in the r ...

s, and higher still are
gamma ray A gamma ray, or 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 and so imparts the hi ...
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 psychoacoustics Psychoacoustics is the branch of psychophysics involving the scientific study of sound perception and audiology—how humans perceive various sounds. More spec ...

. 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 Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular interactions, Physiology, physiological mechanis ...

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 one of several large landmasses. Generally identified by convention (norm), convention rather than any strict criteria, up to seven regions are commonly regarded as continents. Ordered from largest ...

,
Africa Africa is the world's second-largest and second-most populous continent A continent is one of several large landmasses. Generally identified by convention (norm), convention rather than any strict criteria, up to seven regions are ...

,
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, smal ...

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

, most of
Asia Asia () is a landmass variously described as part of Eurasia Eurasia () is the largest continent A continent is any of several large landmasses. Generally identified by convention (norm), convention rather than any strict crite ...
, and
Russia Russia ( rus, link=no, Россия, Rossiya, ), or the Russian Federation, is a country spanning Eastern Europe and Northern Asia. It is the List of countries and dependencies by area, largest country in the world, covering over , and encom ...

, the frequency of the
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 which ...
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 In colorimetry and color theory, lightness, also known as value or tone, is a representation of a color's brightness. It is ...
G), whereas in
North America North America is a continent entirely within the Northern Hemisphere and almost all within the Western Hemisphere. It can also be described as the northern subcontinent of the Americas. It is bordered to the north by the Arctic Ocean, to ...

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 Audio most commonly refers to sound, as it is transmitted in signal form. It may also refer to: Sound *Audio signal, an electrical representation of sound *Audio frequency, a frequency in the audio spectrum *Digital audio, representation of sound ...
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 (mathematics), magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can ...
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, through which its 59 member-states act together on measurement standards in four areas: chemistry, ...

''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 function, periodic vibration whose frequency is in the band audible to the average human, the human hearing range. The International System of Units, SI unit of frequency is the hertz (Hz ...
*
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. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequen ...
*
Cutoff frequency 320px, A Butterworth_filter.html"_;"title="Bode_plot_of_the_Butterworth_filter">Bode_plot_of_the_Butterworth_filter's_frequency_response,_with_corner_frequency_labeled.__(The_slope_−20 dB_per_decade_(log_scale).html" ;"title="frequency_re ...
*
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-element model, lumped electronic components, as opposed to distributed-element filters. That i ...
*
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 ...
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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 ...
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Frequency modulation Frequency modulation (FM) is the encoding of information Information can be thought of as the resolution of uncertainty; it answers the question of "What an entity is" and thus defines both its essence and the nature of its characteristic ...

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Frequency spectrum The power spectrum S_(f) of a time series x(t) describes the distribution of power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In the International System ...
* Interaction frequency *
Least-squares spectral analysis Least-squares spectral analysis (LSSA) is a method of estimating a frequency spectrum The power spectrum S_(f) of a time series x(t) describes the distribution of power Power typically refers to: * Power (physics) In physics, power is t ...
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Natural frequency Natural frequency, also known as eigenfrequency, is the frequency at which a system tends to Oscillation, oscillate in the absence of any driving or Damping ratio, damping force. The motion pattern of a system oscillating at its natural frequency ...
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Negative frequencyThe concept of negative and positive 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 frequency and angular frequency. ...

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Periodicity (disambiguation) Periodicity or periodic may refer to: Mathematics * Bott periodicity theorem In mathematics, the Bott periodicity theorem describes a periodicity in the homotopy groups of classical groups, discovered by , which proved to be of foundational si ...
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Radar signal characteristicsA radar system uses a radio-frequency electromagnetic signal reflected from a target to determine information about that target. In any radar Radar is a detection system that uses radio waves to determine the range, angle, or velocity of ob ...
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Signaling (telecommunications) In telecommunication Telecommunication is the transmission of information Information can be thought of as the resolution of uncertainty; it answers the question of "What an entity is" and thus defines both its essence and the nature o ...
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Spread spectrum In telecommunication and radio communication, spread-spectrum techniques are methods by which a signal (electrical engineering), signal (e.g., an electrical, electromagnetic, or acoustic signal) generated with a particular Bandwidth (signal pr ...
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Spectral componentIn telecommunications, spectral component is any of the waves that range outside the interval of frecy, frequencies assigned to a signal. Any waveform can be disassembled into its spectral components by Fourier analysis or Fourier transformation. The ...
* Transverter *
Upsampling In digital signal processing, upsampling, expansion, and interpolation are terms associated with the process of resampling in a multi-rate digital signal processing system. ''Upsampling'' can be synonymous with ''expansion'', or it can describe an ...
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Orders of magnitude (frequency) The following list illustrates various frequencies 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 frequency and angular freque ...

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