Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light. The interval of time between events is called the period. It is the reciprocal of the frequency. 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 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
For cyclical phenomena such as oscillations, waves, 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) is also used. 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
f = 1 T . {\displaystyle f={\frac {1}{T}}.}
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. The SI unit of frequency is the hertz (Hz), named after the German physicist Heinrich Hertz by the International Electrotechnical Commission in 1930. It was adopted by the CGPM (Conférence générale des poids et mesures) in 1960, officially replacing the previous name, cycle per second (cps). The SI unit for the period, as for all measurements of time, is the second. A traditional unit of frequency used with rotating mechanical devices, where it is termed rotational frequency, is revolution per minute, abbreviated r/min or rpm. Sixty rpm is equivalent to one hertz.
Period versus frequency As a matter of convenience, longer and slower waves, such as ocean surface waves, are more typically described by wave period rather than frequency. Short and fast waves, like audio and radio, are usually described by their frequency. Some commonly used conversions are listed below:
Related quantities
Rotational frequency, usually denoted by the Greek letter ν (nu), is defined as the instantaneous rate of change of the number of rotations, N, with respect to time: ν = dN/dt; it is a type of frequency applied to rotational motion. Angular frequency, usually denoted by the Greek letter ω (omega), is defined as the rate of change of angular displacement (during rotation), θ (theta), or the rate of change of the phase of a sinusoidal waveform (notably in oscillations and waves), or as the rate of change of the argument to the sine function: y ( t ) = sin θ ( t ) = sin ( ω t ) = sin ( 2 π f t ) {\displaystyle y(t)=\sin \theta (t)=\sin(\omega t)=\sin(2\mathrm {\pi } ft)} d θ d t = ω = 2 π f . {\displaystyle {\frac {\mathrm {d} \theta }{\mathrm {d} t}}=\omega =2\mathrm {\pi } f.} The unit of angular frequency is the radian per second (rad/s) but, for discrete-time signals, can also be expressed as radians per sampling interval, which is a dimensionless quantity. Angular frequency is frequency multiplied by 2π. Spatial frequency, denoted here by ξ (xi), is analogous to temporal frequency, but with a spatial measurement replacing time measurement, e.g.: y ( t ) = sin θ ( t , x ) = sin ( ω t + k x ) {\displaystyle y(t)=\sin \theta (t,x)=\sin(\omega t+kx)} d θ d x = k = 2 π ξ . {\displaystyle {\frac {\mathrm {d} \theta }{\mathrm {d} x}}=k=2\pi \xi .}
Spatial period or wavelength is the spatial analog to temporal period.
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, λ (lambda). Even in dispersive media, the frequency f of a sinusoidal wave is equal to the phase velocity v of the wave divided by the wavelength λ of the wave:
f = v λ . {\displaystyle f={\frac {v}{\lambda }}.}
In the special case of electromagnetic waves in vacuum, then v = c, where c is the speed of light in vacuum, and this expression becomes
f = c λ . {\displaystyle f={\frac {c}{\lambda }}.}
When monochromatic waves travel from one medium to another, their frequency remains the same—only their wavelength and speed 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 period. For example, if 71 events occur within 15 seconds the frequency is:
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