Frequency: Difference between revisions

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{{Short description|Number of occurrences or cycles per unit time}}

{{Redirect|Frequencies|other uses|Frequencies (film){{!}}''Frequencies'' (film)|and|Frequencies (album){{!}}''Frequencies'' (album)|and|Frequency (disambiguation)}}

~~{{Short description|Number of occurrences or cycles per unit time}}~~

~~{{Redirect|Frequencies|the film|Frequencies (film){{!}}''Frequencies'' (film)|the album|Frequencies (album){{!}}''Frequencies'' (album)|other uses|Frequency (disambiguation)}}~~

{{Infobox physical quantity

| name = Frequency

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The interval of time between events is called the '''period'''. It is the [[Multiplicative inverse|reciprocal]] of the frequency.<ref>{{cite web|url=http://www.merriam-webster.com/dictionary/period|title=Definition of PERIOD|access-date=3 October 2016}}</ref> For example, if a heart beats at a frequency of 120 times per minute (2 hertz), its period is one half of a second.

Special definitions of frequency are used in certain contexts, such as the [[angular frequency]] in rotational or cyclical properties, when the rate of angular progress is measured. [[Spatial frequency]] is defined for properties that vary or ~~cccur~~ repeatedly in geometry or space.

Special definitions of frequency are used in certain contexts, such as the [[angular frequency]] in rotational or cyclical properties, when the rate of angular progress is measured. [[Spatial frequency]] is defined for properties that vary or occur repeatedly in geometry or space.

The unit of measurement of frequency in the [[International System of Units]] (SI) is the [[hertz]], having the symbol Hz.

== Definitions and units {{anchor|Definitions|Units|Definition|Unit}} ==

[[File:Pendulum-no-text.gif|thumb|A [[pendulum]] with a period of 2.8 s and a frequency of 0.36 [[Hertz|Hz]]]]

For cyclical phenomena such as [[oscillation]]s, [[wave]]s, or for examples of [[simple harmonic motion]], the term ''frequency'' is defined as the number of cycles or repetitions per unit of time. The conventional symbol for frequency is ''f'' or ''ν'' (the Greek letter [[Nu (~~letter~~)|nu]]) is also used.{{sfn|Serway|Faughn|1989|p=346}} The ''period'' ''T'' is the time taken to complete one cycle of an oscillation or rotation. The frequency and the period are related by the equation{{sfn|Serway|Faughn|1989|p=354}}

For cyclical phenomena such as [[oscillation]]s, [[wave]]s, or for examples of [[simple harmonic motion]], the term ''frequency'' is defined as the number of cycles or repetitions per unit of time. The conventional symbol for frequency is ''f'' or ''ν'' (the Greek letter [[Nu (Greek)|nu]]) is also used.{{sfn|Serway|Faughn|1989|p=346}} The ''period'' ''T'' is the time taken to complete one cycle of an oscillation or rotation. The frequency and the period are related by the equation{{sfn|Serway|Faughn|1989|p=354}}

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== Related quantities ==

[[File:~~Commutative diagram of harmonic wave~~ properties.svg|thumb|Diagram of the relationship between the different types of frequency and other wave properties. In this diagram, ''x'' is the input to the function represented by the arrow.]]

[[File:Wave properties.svg|thumb|Diagram of the relationship between the different types of frequency and other wave properties. In this diagram, ''x'' is the input to the function represented by the arrow.]]

* [[Rotational frequency]], usually denoted by the Greek letter [[Nu (~~letter~~)|''ν'']] (nu), is defined as the instantaneous rate of change of the [[number of rotations]], ''N'', with respect to time: {{nowrap|''ν'' {{=}} d''N''/d''t'';}} it is a type of frequency applied to [[rotational motion]].

* [[Rotational frequency]], usually denoted by the Greek letter [[Nu (Greek)|''ν'']] (nu), is defined as the instantaneous rate of change of the [[number of rotations]], ''N'', with respect to time: {{nowrap|''ν'' {{=}} d''N''/d''t'';}} it is a type of frequency applied to [[rotational motion]].

* [[Angular frequency]], usually denoted by the Greek letter [[Omega (letter)|''ω'']] (omega), is defined as the rate of change of [[angular displacement]] (during rotation), [[Theta|''θ'']] (theta), or the rate of change of the [[phase (waves)|phase]] of a [[Sine wave|sinusoid]]al waveform (notably in oscillations and waves), or as the rate of change of the [[Argument of a function|argument]] to the [[sine function]]:

* [[Angular frequency]], usually denoted by the Greek letter [[Omega (letter)|''ω'']] (omega), is defined as the rate of change of [[angular displacement]] (during rotation), [[Theta|''θ'']] (theta), or the rate of change of the [[phase (waves)|phase]] of a [[Sine wave|sinusoid]]al waveform (notably in oscillations and waves), or as the rate of change of the [[Argument of a function|argument]] to the [[sine function]]: <math display="block">y(t) = \sin \theta(t) = \sin(\omega t) = \sin(2 \mathrm{\pi} f t)</math> <math display="block" qid=Q161635>\frac{\mathrm{d} \theta}{\mathrm{d} t} = \omega = 2 \mathrm{\pi} f.</math> The unit of angular frequency is the [[radian]] per second (rad/s) but, for [[discrete-time signal]]s, can also be expressed as radians per [[sampling interval]], which is a [[dimensionless quantity]]. Angular frequency is frequency multiplied by 2{{pi}}.

:<math display="block">y(t) = \sin \theta(t) = \sin(\omega t) = \sin(2 \mathrm{\pi} f t)</math> <math display="block" qid=Q161635>\frac{\mathrm{d} \theta}{\mathrm{d} t} = \omega = 2 \mathrm{\pi} f .</math>

* [[Spatial frequency]], denoted here by ''[[ξ]]'' (xi), is analogous to temporal frequency, but with a spatial measurement replacing time measurement, e.g.: <math display="block">y(t) = \sin \theta(t,x) = \sin(\omega t + kx)</math> <math display="block" qid=Q192510>\frac{\mathrm{d} \theta}{\mathrm{d} x} = k = 2 \pi \xi.</math>

: The unit of angular frequency is the [[radian]] per second (rad/s) but, for [[discrete-time signal]]s, can also be expressed as radians per [[sampling interval]], which is a [[dimensionless quantity]]. Angular frequency is frequency multiplied by 2{{pi}}.

** [[Spatial period]] or wavelength is the spatial analog to temporal period.<ref>{{cite web |last1=Boreman |first1=Glenn D. |title=Spatial Frequency |url=https://spie.org/publications/tt52_12_spatial_frequency?SSO=1 |publisher=[[SPIE]] |access-date=22 January 2021}}</ref>

* [[Spatial frequency]], denoted here by ''[[ξ]]'' (xi), is analogous to temporal frequency, but with a spatial measurement replacing time measurement,{{refn|1=The term ''spatial period'', sometimes used in place of ''[[wavelength]]'', analogously corresponds to the (temporal) period.<ref>{{cite web |last1=Boreman |first1=Glenn D. |title=Spatial Frequency |url=https://spie.org/publications/tt52_12_spatial_frequency?SSO=1 |publisher=[[SPIE]] |access-date=22 January 2021}}</ref>|group=note}} e.g.: <math display="block">y(t) = \sin \theta(t,x) = \sin(\omega t + kx)</math> <math display="block" qid=Q192510>\frac{\mathrm{d} \theta}{\mathrm{d} x} = k = 2 \pi \xi.</math>

** [[Spatial period]] or wavelength is the spatial analog to temporal period.

== In wave propagation {{anchor|Frequency of waves}} ==

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For periodic waves in [[Dispersion relation|nondispersive media]] (that is, media in which the wave speed is independent of frequency), frequency has an inverse relationship to the [[wavelength]], ''λ'' ([[lambda]]). Even in dispersive media, the frequency ''f'' of a [[Sine wave|sinusoidal wave]] is equal to the [[phase velocity]] ''v'' of the wave [[division (mathematics)|divided]] by the wavelength ''λ'' of the wave:

For periodic waves in [[Dispersion relation|nondispersive media]] (that is, media in which the wave speed is independent of frequency), frequency has an inverse relationship to the [[wavelength]], ''λ'' ([[lambda]]).<ref>{{Cite book |last=Shankar |first=Ramamurti |title=Fundamentals of physics I: mechanics, relativity, and thermodynamics |date=2019 |publisher=Yale University Press |isbn=978-0-300-24377-2 |edition=Expanded |series=The open Yale courses series |location=New Haven}}</ref> Even in dispersive media, the frequency ''f'' of a [[Sine wave|sinusoidal wave]] is equal to the [[phase velocity]] ''v'' of the wave [[division (mathematics)|divided]] by the wavelength ''λ'' of the wave:<ref>{{Cite book |last=French |first=Anthony |title=Vibrations and Waves |publisher=CBS Publishers & Distributors Pvt Ltd, India |year=1987 |isbn=978-8123909141}}</ref>

f = \frac{v}{\lambda}.

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</math>

When [[monochromatic radiation|monochromatic waves]] travel from one [[medium (optics)|medium]] to another, their frequency remains the same—only their wavelength and [[phase speed|speed]] change.

When [[monochromatic radiation|monochromatic waves]] travel from one [[medium (optics)|medium]] to another, their frequency remains the same—only their wavelength and [[phase speed|speed]] change.<ref>{{Cite book |last=Serway |first=Raymond |title=Physics for Scientists and Engineers with Modern Physics |last2=Jewett |first2=John |publisher=Mary Finch |year=2010 |isbn=978-1-4390-4844-3 |edition=8th}}</ref>

== Measurement ==

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=== 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 period. For example, if 71 events occur within 15 seconds the frequency is:

<math display=block>f = \frac{71}{15 \,\text{s}} \approx 4.73 \, \text{Hz}.</math>

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.{{cn|date=April 2024}} The latter method introduces a [[random error]] into the count of between zero and one count, so on [[average]] half a count. This is called ''gating error'' and causes an average error in the calculated frequency of <math display="inline">\Delta f = \frac{1}{2T_\text{m}}</math>, or a fractional error of <math display="inline">\frac{\Delta f}{f} = \frac{1}{2 f T_\text{m}}</math> where <math>T_\text{m}</math> is the timing interval and <math>f</math> 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.

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.{{citation needed|date=April 2024}} The latter method introduces a [[random error]] into the count of between zero and one count, so on [[average]] half a count. This is called ''gating error'' and causes an average error in the calculated frequency of <math display="inline">\Delta f = \frac{1}{2T_\text{m}}</math>, or a fractional error of <math display="inline">\frac{\Delta f}{f} = \frac{1}{2 f T_\text{m}}</math> where <math>T_\text{m}</math> is the timing interval and <math>f</math> 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.

{{multiple image

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=== Light ===

[[File:EM spectrum.svg|thumb|upright=2|Complete spectrum of [[electromagnetic radiation]] with the visible portion highlighted]]

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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]]. They all travel through vacuum at the same speed (the speed of light), giving them wavelengths inversely proportional to their frequencies.

<math display=block qid=Q2111>\displaystyle c=f\lambda,</math>

where ''c'' is the speed of light (''c'' in vacuum or less in other media), ''f'' is the frequency and ''λ'' is the wavelength.

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=== Sound ===

[[File:Ultrasound range diagram.svg|thumb|upright=1.7|The [[sound wave]] spectrum, with rough guide of some applications]]

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=== Line current ===

In [[Europe]], [[Africa]], [[Australia]], southern [[South America]], most of [[Asia]], and [[Russia]], the frequency of the [[alternating current]] in [[mains electricity|household electrical outlets]] is 50 Hz (close to the [[Musical note|tone]] G), whereas in [[North America]] and northern South America, the frequency of the alternating current in household electrical outlets is 60 Hz (between the tones B{{music|♭}} and B; that is, a [[minor third]] above the European frequency). The frequency of the '[[mains hum|hum]]' in an [[audio recording]] can show in which of these general regions the recording was made.

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'''Aperiodic frequency''' is the [[rate (mathematics)|rate]] of incidence or occurrence of non-[[Periodic function|cyclic]] phenomena, including random processes such as [[radioactive decay]]. It is expressed with the unit [[reciprocal second]] (s<sup>−1</sup>)<ref>{{Cite book |title=Mechatronic Systems, Sensors, and Actuators: Fundamentals and Modeling |last=Lombardi |first=Michael A. |publisher=CRC Press |year=2007 |isbn=9781420009002 |editor-last=Bishop |editor-first=Robert H. |location=Austin |language=en|chapter=Fundamentals of Time and Frequency}}</ref> or, in the case of radioactivity, with the unit [[becquerel]].<ref>{{cite report | last1=Newell | first1=David B | last2=Tiesinga | first2=Eite | title=The international system of units (SI) | publisher=National Institute of Standards and Technology | publication-place=Gaithersburg, MD | year=2019 | doi=10.6028/nist.sp.330-2019 | url = https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.330-2019.pdf}} sub§2.3.4, Table 4.</ref>

It is ~~defined~~ as a [[~~rate (mathematics)|rate~~]], {{nowrap|1=''f'' = ''N''/Δ''t''}}, involving the [[number of entities]] counted or the number of [[Event (philosophy)|event]]s happened (''N'') during a given [[Time|time duration]] (Δ''t'');<ref>{{Cite web |title=SI Brochure |url=https://www.bipm.org/en/publications/si-brochure |access-date=2025-04-24 |website=BIPM |language=en-US}}</ref> it is a [[physical quantity]] of type [[temporal rate]].

It is formulated as a [[quotient]],

:{{nowrap|1=''f'' = ''N''/Δ''t''}},

involving the [[number of entities]] counted or the number of [[Event (philosophy)|event]]s happened (''N'') during a given [[Time|time duration]] (Δ''t'');<ref>{{Cite web |title=SI Brochure |url=https://www.bipm.org/en/publications/si-brochure |access-date=2025-04-24 |website=BIPM |language=en-US}}</ref> it is a [[physical quantity]] of type [[temporal rate]].

== See also ==

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[[Category:Frequency|*]]

[[Category:Frequency| ]]

@@ Line 1: / Line 1: @@
+{{Short description|Number of occurrences or cycles per unit time}}
+{{Redirect|Frequencies|other uses|Frequencies (film){{!}}''Frequencies'' (film)|and|Frequencies (album){{!}}''Frequencies'' (album)|and|Frequency (disambiguation)}}
 {{more citations needed|date=May 2025}}
-{{Short description|Number of occurrences or cycles per unit time}}
-{{Redirect|Frequencies|the film|Frequencies (film){{!}}''Frequencies'' (film)|the album|Frequencies (album){{!}}''Frequencies'' (album)|other uses|Frequency (disambiguation)}}
 {{Infobox physical quantity
 | name = Frequency
@@ Line 25: / Line 25: @@
 The interval of time between events is called the '''period'''. It is the [[Multiplicative inverse|reciprocal]] of the frequency.<ref>{{cite web|url=http://www.merriam-webster.com/dictionary/period|title=Definition of PERIOD|access-date=3 October 2016}}</ref>  For example, if a heart beats at a frequency of 120 times per minute (2&nbsp;hertz), its period is one half of a second.
-Special definitions of frequency are used in certain contexts, such as the [[angular frequency]] in rotational or cyclical properties, when the rate of angular progress is measured. [[Spatial frequency]] is defined for properties that vary or cccur repeatedly in geometry or space.
+Special definitions of frequency are used in certain contexts, such as the [[angular frequency]] in rotational or cyclical properties, when the rate of angular progress is measured. [[Spatial frequency]] is defined for properties that vary or occur repeatedly in geometry or space.
 The unit of measurement of frequency in the [[International System of Units]] (SI) is the [[hertz]], having the symbol Hz.
 == Definitions and units {{anchor|Definitions|Units|Definition|Unit}} ==
 [[File:Pendulum-no-text.gif|thumb|A [[pendulum]] with a period of 2.8&nbsp;s and a frequency of 0.36&nbsp;[[Hertz|Hz]]]]
-For cyclical phenomena such as [[oscillation]]s, [[wave]]s, or for examples of [[simple harmonic motion]], the term ''frequency'' is defined as the number of cycles or repetitions per unit of time. The conventional symbol for frequency is ''f'' or ''ν'' (the Greek letter [[Nu (letter)|nu]]) is also used.{{sfn|Serway|Faughn|1989|p=346}} The ''period'' ''T'' is the time taken to complete one cycle of an oscillation or rotation. The frequency and the period are related by the equation{{sfn|Serway|Faughn|1989|p=354}}
+For cyclical phenomena such as [[oscillation]]s, [[wave]]s, or for examples of [[simple harmonic motion]], the term ''frequency'' is defined as the number of cycles or repetitions per unit of time. The conventional symbol for frequency is ''f'' or ''ν'' (the Greek letter [[Nu (Greek)|nu]]) is also used.{{sfn|Serway|Faughn|1989|p=346}} The ''period'' ''T'' is the time taken to complete one cycle of an oscillation or rotation. The frequency and the period are related by the equation{{sfn|Serway|Faughn|1989|p=354}}
 <math display=block qid=Q11652>f = \frac{1}{T}.</math>
@@ Line 67: / Line 68: @@
 == Related quantities ==
-[[File:Commutative diagram of harmonic wave properties.svg|thumb|Diagram of the relationship between the different types of frequency and other wave properties.  In this diagram, ''x'' is the input to the function represented by the arrow.]]
+[[File:Wave properties.svg|thumb|Diagram of the relationship between the different types of frequency and other wave properties.  In this diagram, ''x'' is the input to the function represented by the arrow.]]
-* [[Rotational frequency]], usually denoted by the Greek letter [[Nu (letter)|''ν'']] (nu), is defined as the instantaneous rate of change of the [[number of rotations]], ''N'', with respect to time: {{nowrap|''ν'' {{=}} d''N''/d''t'';}} it is a type of frequency applied to [[rotational motion]].
+* [[Rotational frequency]], usually denoted by the Greek letter [[Nu (Greek)|''ν'']] (nu), is defined as the instantaneous rate of change of the [[number of rotations]], ''N'', with respect to time: {{nowrap|''ν'' {{=}} d''N''/d''t'';}} it is a type of frequency applied to [[rotational motion]].
-* [[Angular frequency]], usually denoted by the Greek letter [[Omega (letter)|''ω'']] (omega), is defined as the rate of change of [[angular displacement]] (during rotation), [[Theta|''θ'']] (theta), or the rate of change of the [[phase (waves)|phase]] of a [[Sine wave|sinusoid]]al waveform (notably in oscillations and waves), or as the rate of change of the [[Argument of a function|argument]] to the [[sine function]]:
+* [[Angular frequency]], usually denoted by the Greek letter [[Omega (letter)|''ω'']] (omega), is defined as the rate of change of [[angular displacement]] (during rotation), [[Theta|''θ'']] (theta), or the rate of change of the [[phase (waves)|phase]] of a [[Sine wave|sinusoid]]al waveform (notably in oscillations and waves), or as the rate of change of the [[Argument of a function|argument]] to the [[sine function]]: <math display="block">y(t) = \sin \theta(t)  =  \sin(\omega t) =  \sin(2 \mathrm{\pi} f t)</math> <math display="block" qid=Q161635>\frac{\mathrm{d} \theta}{\mathrm{d} t} = \omega = 2 \mathrm{\pi} f.</math> The unit of angular frequency is the [[radian]] per second (rad/s) but, for [[discrete-time signal]]s, can also be expressed as radians per [[sampling interval]], which is a [[dimensionless quantity]]. Angular frequency is frequency multiplied by 2{{pi}}.
-:<math display="block">y(t) = \sin \theta(t)  =  \sin(\omega t) =  \sin(2 \mathrm{\pi} f t)</math> <math display="block" qid=Q161635>\frac{\mathrm{d} \theta}{\mathrm{d} t} = \omega = 2 \mathrm{\pi} f .</math>
+* [[Spatial frequency]], denoted here by ''[[ξ]]'' (xi), is analogous to temporal frequency, but with a spatial measurement replacing time measurement, e.g.: <math display="block">y(t) = \sin \theta(t,x) = \sin(\omega t + kx)</math> <math display="block" qid=Q192510>\frac{\mathrm{d} \theta}{\mathrm{d} x} = k = 2 \pi \xi.</math>
-: The unit of angular frequency is the [[radian]] per second (rad/s) but, for [[discrete-time signal]]s, can also be expressed as radians per [[sampling interval]], which is a [[dimensionless quantity]]. Angular frequency is frequency multiplied by 2{{pi}}.
+** [[Spatial period]] or wavelength is the spatial analog to temporal period.<ref>{{cite web |last1=Boreman |first1=Glenn D. |title=Spatial Frequency |url=https://spie.org/publications/tt52_12_spatial_frequency?SSO=1 |publisher=[[SPIE]] |access-date=22 January 2021}}</ref>
-* [[Spatial frequency]], denoted here by ''[[ξ]]'' (xi), is analogous to temporal frequency, but with a spatial measurement replacing time measurement,{{refn|1=The term ''spatial period'', sometimes used in place of ''[[wavelength]]'', analogously corresponds to the (temporal) period.<ref>{{cite web |last1=Boreman |first1=Glenn D. |title=Spatial Frequency |url=https://spie.org/publications/tt52_12_spatial_frequency?SSO=1 |publisher=[[SPIE]] |access-date=22 January 2021}}</ref>|group=note}} e.g.: <math display="block">y(t) = \sin \theta(t,x) = \sin(\omega t + kx)</math> <math display="block" qid=Q192510>\frac{\mathrm{d} \theta}{\mathrm{d} x} = k = 2 \pi \xi.</math>
-** [[Spatial period]] or wavelength is the spatial analog to temporal period.
 == In wave propagation {{anchor|Frequency of waves}} ==
@@ Line 79: / Line 78: @@
 {{Further|Wave propagation}}
 <!-- This section is linked from [[Hearing impairment]] -->
-For periodic waves in [[Dispersion relation|nondispersive media]] (that is, media in which the wave speed is independent of frequency), frequency has an inverse relationship to the [[wavelength]], ''λ'' ([[lambda]]). Even in dispersive media, the frequency ''f'' of a [[Sine wave|sinusoidal wave]] is equal to the [[phase velocity]] ''v'' of the wave [[division (mathematics)|divided]] by the wavelength ''λ'' of the wave:
+For periodic waves in [[Dispersion relation|nondispersive media]] (that is, media in which the wave speed is independent of frequency), frequency has an inverse relationship to the [[wavelength]], ''λ'' ([[lambda]]).<ref>{{Cite book |last=Shankar |first=Ramamurti |title=Fundamentals of physics I: mechanics, relativity, and thermodynamics |date=2019 |publisher=Yale University Press |isbn=978-0-300-24377-2 |edition=Expanded |series=The open Yale courses series |location=New Haven}}</ref> Even in dispersive media, the frequency ''f'' of a [[Sine wave|sinusoidal wave]] is equal to the [[phase velocity]] ''v'' of the wave [[division (mathematics)|divided]] by the wavelength ''λ'' of the wave:<ref>{{Cite book |last=French |first=Anthony |title=Vibrations and Waves |publisher=CBS Publishers & Distributors Pvt Ltd, India |year=1987 |isbn=978-8123909141}}</ref>
 <math display=block>
 f = \frac{v}{\lambda}.
@@ Line 89: / Line 89: @@
 </math>
-When [[monochromatic radiation|monochromatic waves]] travel from one [[medium (optics)|medium]] to another, their frequency remains the same—only their wavelength and [[phase speed|speed]] change.
+When [[monochromatic radiation|monochromatic waves]] travel from one [[medium (optics)|medium]] to another, their frequency remains the same—only their wavelength and [[phase speed|speed]] change.<ref>{{Cite book |last=Serway |first=Raymond |title=Physics for Scientists and Engineers with Modern Physics |last2=Jewett |first2=John |publisher=Mary Finch |year=2010 |isbn=978-1-4390-4844-3 |edition=8th}}</ref>
 == Measurement ==
-{{unreferenced|section|date=May 2025}}
+{{unreferenced section|date=May 2025}}
 {{See also|Frequency meter}}
@@ Line 99: / Line 99: @@
 === 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 period. For example, if 71 events occur within 15 seconds the frequency is:
 <math display=block>f = \frac{71}{15 \,\text{s}} \approx 4.73 \, \text{Hz}.</math>
-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.{{cn|date=April 2024}} The latter method introduces a [[random error]] into the count of between zero and one count, so on [[average]] half a count. This is called ''gating error'' and causes an average error in the calculated frequency of <math display="inline">\Delta f = \frac{1}{2T_\text{m}}</math>, or a fractional error of <math display="inline">\frac{\Delta f}{f} = \frac{1}{2 f T_\text{m}}</math> where <math>T_\text{m}</math> is the timing interval and <math>f</math> 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.
+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.{{citation needed|date=April 2024}} The latter method introduces a [[random error]] into the count of between zero and one count, so on [[average]] half a count. This is called ''gating error'' and causes an average error in the calculated frequency of <math display="inline">\Delta f = \frac{1}{2T_\text{m}}</math>, or a fractional error of <math display="inline">\frac{\Delta f}{f} = \frac{1}{2 f T_\text{m}}</math> where <math>T_\text{m}</math> is the timing interval and <math>f</math> 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.
 {{multiple image
@@ Line 129: / Line 131: @@
 === Light ===
-{{main article|Light|Electromagnetic radiation}}
+{{main|Light|Electromagnetic radiation}}
 <!--Linked from [[Neil Harbisson]]-->
 [[File:EM spectrum.svg|thumb|upright=2|Complete spectrum of [[electromagnetic radiation]] with the visible portion highlighted]]
@@ Line 136: / Line 138: @@
 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]]. They all travel through vacuum at the same speed (the speed of light), giving them wavelengths inversely proportional to their frequencies.
 <math display=block qid=Q2111>\displaystyle c=f\lambda,</math>
 where ''c'' is the speed of light (''c'' in vacuum or less in other media), ''f'' is the frequency and ''λ'' is the wavelength.
@@ Line 142: / Line 146: @@
 === Sound ===
-{{main article|Audio frequency}}
+{{main|Audio frequency}}
 [[File:Ultrasound range diagram.svg|thumb|upright=1.7|The [[sound wave]] spectrum, with rough guide of some applications]]
@@ Line 163: / Line 167: @@
 === Line current ===
-{{main article|Utility frequency}}
+{{main|Utility frequency}}
 In [[Europe]], [[Africa]], [[Australia]], southern [[South America]], most of [[Asia]], and [[Russia]], the frequency of the [[alternating current]] in [[mains electricity|household electrical outlets]] is 50&nbsp;Hz (close to the [[Musical note|tone]] G), whereas in [[North America]] and northern South America, the frequency of the alternating current in household electrical outlets is 60&nbsp;Hz (between the tones B{{music|♭}} and B; that is, a [[minor third]] above the European frequency). The frequency of the '[[mains hum|hum]]' in an [[audio recording]] can show in which of these general regions the recording was made.
@@ Line 169: / Line 173: @@
 '''Aperiodic frequency''' is the [[rate (mathematics)|rate]] of incidence or occurrence of non-[[Periodic function|cyclic]] phenomena, including random processes such as [[radioactive decay]]. It is expressed with the unit [[reciprocal second]] (s<sup>−1</sup>)<ref>{{Cite book |title=Mechatronic Systems, Sensors, and Actuators: Fundamentals and Modeling |last=Lombardi |first=Michael A. |publisher=CRC Press |year=2007 |isbn=9781420009002 |editor-last=Bishop |editor-first=Robert H. |location=Austin |language=en|chapter=Fundamentals of Time and Frequency}}</ref> or, in the case of radioactivity, with the unit [[becquerel]].<ref>{{cite report | last1=Newell | first1=David B | last2=Tiesinga | first2=Eite | title=The international system of units (SI) | publisher=National Institute of Standards and Technology | publication-place=Gaithersburg, MD | year=2019 | doi=10.6028/nist.sp.330-2019 | url = https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.330-2019.pdf}} sub§2.3.4, Table 4.</ref>
-It is defined as a [[rate (mathematics)|rate]], {{nowrap|1=''f'' = ''N''/Δ''t''}}, involving the [[number of entities]] counted or the number of [[Event (philosophy)|event]]s happened (''N'') during a given [[Time|time duration]] (Δ''t'');<ref>{{Cite web |title=SI Brochure |url=https://www.bipm.org/en/publications/si-brochure |access-date=2025-04-24 |website=BIPM |language=en-US}}</ref> it is a [[physical quantity]] of type [[temporal rate]].
+It is formulated as a [[quotient]],
+:{{nowrap|1=''f'' = ''N''/Δ''t''}},
+involving the [[number of entities]] counted or the number of [[Event (philosophy)|event]]s happened (''N'') during a given [[Time|time duration]] (Δ''t'');<ref>{{Cite web |title=SI Brochure |url=https://www.bipm.org/en/publications/si-brochure |access-date=2025-04-24 |website=BIPM |language=en-US}}</ref> it is a [[physical quantity]] of type [[temporal rate]].
 == See also ==
@@ Line 230: / Line 236: @@
 {{Authority control}}
-[[Category:Frequency|*]]
+[[Category:Frequency| ]]

Frequency: Difference between revisions

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