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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. Frequency is measured in units of hertz (Hz) which is equal to one occurrence of a repeating event per second. The period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example: if a newborn baby's heart beats at a frequency of 120 times a minute (2 hertz), its period, T , — the time interval between beats—is half a second (60 seconds divided by 120 beats). 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.

For cyclical processes, such as rotation, oscillations, or waves, frequency is defined as a number of cycles per unit time. In physics and engineering disciplines, such as optics, acoustics, and radio, frequency is usually denoted by a Latin letter f or by the Greek letter ν {\displaystyle \nu } or ν (nu) (see e.g. Planck's formula). The relation between the frequency and the period, T {\displaystyle T} , of a repeating event or oscillation is given by f = 1 T . {\displaystyle f={\frac {1}{T}}.}

The SI derived unit of frequency is the hertz (Hz), named after the German physicist Heinrich Hertz. One hertz means that an event repeats once per second. If a TV has a refresh rate of 1 hertz the TV screen will change (or refresh) its picture once per second. A previous name for this unit was cycles per second (cps). The SI unit for the period is the second. A traditional unit of measure used with rotating mechanical devices is revolutions per minute, abbreviated r/min or rpm. 60 rpm equals one hertz.

As a matter of convenience, longer and slower waves, such as ocean surface waves, tend to be described by wave period rather than frequency. Short and fast waves, like audio and radio, are usually described by their frequency instead of period. These commonly used conversions are listed below: Frequency 1 mHz (10−3 Hz) 1 Hz (100 Hz) 1 kHz (103 Hz) 1 MHz (106 Hz) 1 GHz (109 Hz) 1 THz (1012 Hz) Period 1 ks (103 s) 1 s (100 s) 1 ms (10−3 s) 1 µs (10−6 s) 1 ns (10−9 s) 1 ps (10−12 s)

Angular frequency, usually denoted by the Greek letter ω (omega), is defined as the rate of change of angular displacement, θ , (during rotation), 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 \left(\theta (t)\right)=\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} Angular frequency is commonly measured in radians 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 (in radians) is larger than regular frequency (in Hz) by a factor of 2π. Spatial frequency is analogous to temporal frequency, but the time axis is ...

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 moving through a vacuum, then v = c , where c is the speed of light in a vacuum, and this expression becomes: f = c λ . {\displaystyle f={\frac {c}{\lambda }}.} When waves from a monochrome source travel from one medium to another, their frequency remains the same—only their wavelength and speed change.

Measurement of frequency can be done in the following ways, Counting edit 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 = 71 15 s ≈ 4.73 Hz {\displaystyle f={\frac {71}{15\,{\text{s}}}}\approx 4.73\,{\text{Hz}}} 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 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 Δ f = 1 2 T m {\displaystyle \Delta f={\frac {1}{2T_{m}}}} , or a fractional error of Δ f f =...

Light edit Visible light is an electromagnetic wave, consisting of oscillating electric and magnetic fields traveling through space. The frequency of the wave determines its color: 4 × 1014 Hz is red light, 8 × 1014 Hz is violet light, and between these (in the range 4- 8 × 1014 Hz ) are all the other colors of the visible spectrum. An electromagnetic wave can have a frequency less than 4 × 1014 Hz , but it will be invisible to the human eye; such waves are called infrared (IR) radiation. At even lower frequency, the wave is called a microwave, and at still lower frequencies it is called a radio wave. Likewise, an electromagnetic wave can have a frequency higher than 8 × 1014 Hz , but it will be invisible to the human eye; such waves are called ultraviolet (UV) radiation. Even higher-frequency waves are called X-rays, and higher still are gamma rays. All of these waves, from the lowest-frequency radio waves to the highest-frequency gamma rays, are fundamentally the same, and they are...