Frequency

== 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.]]
* [[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]].
* [[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}}.
* [[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.