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frequency | |
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Common symbols | f, ν |

SI unit | Hz |

In SI base units | s ^{−1} |

**Frequency** is the number of occurrences of a repeating event per unit of time.^{ [1] } It is also referred to as **temporal frequency**, which emphasizes the contrast to spatial frequency and angular frequency. The

A **unit of time** or **midst unit** is any particular time interval, used as a standard way of measuring or expressing duration. The base **unit of time** in the International System of Units (SI), and by extension most of the Western world, is the second, defined as about 9 billion oscillations of the caesium atom. The exact modern definition, from the National Institute of Standards and Technology is:

In mathematics, physics, and engineering, **spatial frequency** is a characteristic of any structure that is periodic across position in space. The spatial frequency is a measure of how often sinusoidal components of the structure repeat per unit of distance. The SI unit of spatial frequency is cycles per meter. In image-processing applications, spatial frequency is often expressed in units of cycles per millimeter or equivalently line pairs per millimeter.

In physics, **angular frequency***ω* is a scalar measure of rotation rate. It refers to the angular displacement per unit time or the rate of change of the phase of a sinusoidal waveform, or as the rate of change of the argument of the sine function.

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 * or **ν* (nu) (see e.g. Planck's formula).

A **turn** is a unit of plane angle measurement equal to 2π radians, 360 degrees or 400 gradians. A turn is also referred to as a **cycle**, **revolution**, **complete rotation** or **full circle**.

A **rotation** is a circular movement of an object around a center of rotation. A three-dimensional object can always be rotated around an infinite number of imaginary lines called *rotation axes*. If the axis passes through the body's center of mass, the body is said to rotate upon itself, or spin. A rotation about an external point, e.g. the Earth about the Sun, is called a revolution or orbital revolution, typically when it is produced by gravity. The axis is called a **pole**.

**Oscillation** is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. The term *vibration* is precisely used to describe mechanical oscillation. Familiar examples of oscillation include a swinging pendulum and alternating current.

The relation between the frequency and the period of a repeating event or oscillation is given by

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's screen will change (or refresh) its picture once a second. A previous name for this unit was cycles per second (cps). The SI unit for period is the second.

**SI derived units** are units of measurement derived from the seven base units specified by the International System of Units (SI). They are either dimensionless or can be expressed as a product of one or more of the base units, possibly scaled by an appropriate power of exponentiation.

The **hertz** (symbol: **Hz**) is the derived unit of frequency in the International System of Units (SI) and is defined as one cycle per second. It is named for Heinrich Rudolf Hertz, the first person to provide conclusive proof of the existence of electromagnetic waves. Hertz are commonly expressed in multiples: kilohertz (10^{3} Hz, kHz), megahertz (10^{6} Hz, MHz), gigahertz (10^{9} Hz, GHz), terahertz (10^{12} Hz, THz), petahertz (10^{15} Hz, PHz), and exahertz (10^{18} Hz, EHz).

**Heinrich Rudolf Hertz** was a German physicist who first conclusively proved the existence of the electromagnetic waves theorized by James Clerk Maxwell's electromagnetic theory of light. The unit of frequency, cycle per second, was named the "Hertz" in his honor.

A traditional unit of measure used with rotating mechanical devices is revolutions per minute, abbreviated r/min or rpm. 60 rpm equals one hertz.^{ [3] }

**Revolutions per minute** is the number of turns in one minute. It is a unit of rotational speed or the frequency of rotation around a fixed axis.

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:

In physics, **sound** is a vibration that typically propagates as an audible wave of pressure, through a transmission medium such as a gas, liquid or solid.

**Radio** is the technology of using radio waves to carry information, such as sound and images, by systematically modulating properties of electromagnetic energy waves transmitted through space, such as their amplitude, frequency, phase, or pulse width. When radio waves strike an electrical conductor, the oscillating fields induce an alternating current in the conductor. The information in the waves can be extracted and transformed back into its original form.

Frequency | 1 mHz (10^{−3} Hz) | 1 Hz (10^{0} Hz) | 1 kHz (10^{3} Hz) | 1 MHz (10^{6} Hz) | 1 GHz (10^{9} Hz) | 1 THz (10^{12} Hz) |
---|---|---|---|---|---|---|

Period | 1 ks (10^{3} s) | 1 s (10^{0} 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:

**Angular displacement** of a body is the angle in radians through which a point revolves around a centre or line has been rotated in a specified sense about a specified axis. When a body rotates about its axis, the motion cannot simply be analyzed as a particle, as in circular motion it undergoes a changing velocity and acceleration at any time (*t*). When dealing with the rotation of a body, it becomes simpler to consider the body itself rigid. A body is generally considered rigid when the separations between all the particles remains constant throughout the body's motion, so for example parts of its mass are not flying off. In a realistic sense, all things can be deformable, however this impact is minimal and negligible. Thus the rotation of a rigid body over a fixed axis is referred to as rotational motion.

**Phase** is the position of a point in time on a waveform cycle. A complete cycle is defined as the interval required for the waveform to return to its arbitrary initial value. The graph to the right shows how one cycle constitutes 360° of phase. The graph also shows how phase is sometimes expressed in radians, where one radian of phase equals approximately 57.3°.

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 pure and applied mathematics, as well as physics, engineering, signal processing and many other fields. Its most basic form as a function of time (*t*) is**:**

- 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 replaced by one or more spatial displacement axes. E.g.:

- Wavenumber,
*k*, is the spatial frequency analogue of angular temporal frequency and is measured in radians per meter. In the case of more than one spatial dimension, wavenumber is a vector quantity.

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:

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:

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 done in the following ways,

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:

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.^{ [4] } 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 , or a fractional error of where is the timing interval and 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.

An older method of measuring the frequency of rotating or vibrating objects is to use a stroboscope. This is an intense repetitively flashing light (strobe light) 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 integral multiple of the strobing frequency will also appear stationary.

Higher frequencies are usually measured with a frequency counter. This is an electronic instrument which measures the frequency of an applied repetitive electronic signal and displays the result in hertz on a digital display. It uses digital logic to count the number of cycles during a time interval established by a precision quartz time base. Cyclic processes that are not electrical in nature, such as the rotation rate of a shaft, mechanical vibrations, or sound waves, can be converted to a repetitive electronic signal by transducers 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.

Above the range of frequency counters, frequencies of electromagnetic signals are often measured indirectly by means of heterodyning (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. This creates a heterodyne 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).

Visible light is an electromagnetic wave, consisting of oscillating electric and magnetic fields traveling through space. The frequency of the wave determines its color: ×10^{14} Hz is red light, 4×10^{14} Hz is violet light, and between these (in the range 4- 8×10^{14} Hz) are all the other colors of the 8visible spectrum. An electromagnetic wave can have a frequency less than ×10^{14} Hz, but it will be invisible to the human eye; such waves are called 4infrared (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 ×10^{14} Hz, but it will be invisible to the human eye; such waves are called 8ultraviolet (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 all called electromagnetic radiation. They all travel through a vacuum at the same speed (the speed of light), giving them wavelengths inversely proportional to their frequencies.

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 propagates as mechanical vibration waves of pressure and displacement, in air or other substances.^{ [5] }. In general, frequency components of a sound determine its "color", its timbre. When speaking about the frequency (in singular) of a sound, it means the property that most determines pitch.^{ [6] }

The frequencies an ear can hear are limited to a specific range of frequencies. The audible frequency 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 have different hearing ranges. For example, some dog breeds can perceive vibrations up to 60,000 Hz.^{ [7] }

In many media, such as air, the speed of sound is approximately independent of frequency, so the wavelength of the sound waves (distance between repetitions) is approximately inversely proportional to frequency.

In Europe, Africa, Australia, Southern South America, most of Asia, and Russia, the frequency of the alternating current in household electrical outlets is 50 Hz (close to the 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♭ and B; that is, a minor third above the European frequency). The frequency of the 'hum' in an audio recording can show where the recording was made, in countries using a European, or an American, grid frequency.

- Audio frequency
- Bandwidth (signal processing)
- Cutoff frequency
- Downsampling
- Electronic filter
- Frequency band
- Frequency converter
- Frequency domain
- Frequency distribution
- Frequency extender
- Frequency grid
- Frequency modulation
- Frequency spectrum
- Interaction frequency
- Natural frequency
- Negative frequency
- Periodicity (disambiguation)
- Pink noise
- Preselector
- Radar signal characteristics
- Signaling (telecommunications)
- Spread spectrum
- Spectral component
- Transverter
- Upsampling

- ↑ "Definition of FREQUENCY" . Retrieved 3 October 2016.
- ↑ "Definition of PERIOD" . Retrieved 3 October 2016.
- ↑ Davies, A. (1997).
*Handbook of Condition Monitoring: Techniques and Methodology*. New York: Springer. ISBN 978-0-412-61320-3. - ↑ Bakshi, K.A.; A.V. Bakshi; U.A. Bakshi (2008).
*Electronic Measurement Systems*. US: Technical Publications. pp. 4–14. ISBN 978-81-8431-206-5. - ↑ "Definition of SOUND" . Retrieved 3 October 2016.
- ↑ Pilhofer, Michael (2007).
*Music Theory for Dummies*. For Dummies. p. 97. ISBN 9780470167946. - ↑ Elert, Glenn; Timothy Condon (2003). "Frequency Range of Dog Hearing". The Physics Factbook. Retrieved 2008-10-22.

- Giancoli, D.C. (1988).
*Physics for Scientists and Engineers*(2nd ed.). Prentice Hall. ISBN 978-0-13-669201-0.

Look up or frequency in Wiktionary, the free dictionary. often |

- Conversion: frequency to wavelength and back
- Conversion: period, cycle duration, periodic time to frequency
- Keyboard frequencies = naming of notes - The English and American system versus the German system
- Teaching resource for 14-16yrs on sound including frequency
- A simple tutorial on how to build a frequency meter
- Frequency - diracdelta.co.uk – JavaScript calculation.
- A frequency generator with sound, useful for hearing tests

When two particles interact, their mutual **cross section** is the area transverse to their relative motion within which they must meet in order to scatter from each other. If the particles are hard inelastic spheres that interact only upon contact, their scattering cross section is related to their geometric size. If the particles interact through some action-at-a-distance force, such as electromagnetism or gravity, their scattering cross section is generally larger than their geometric size. When a cross section is specified as a function of some final-state variable, such as particle angle or energy, it is called a **differential cross section**. When a cross section is integrated over all scattering angles, it is called a **total cross section**. Cross sections are typically denoted *σ* (sigma) and measured in units of area.

The **fundamental frequency**, often referred to simply as the **fundamental**, is defined as the lowest frequency of a periodic waveform. In music, the fundamental is the musical pitch of a note that is perceived as the lowest partial present. In terms of a superposition of sinusoids, the fundamental frequency is the lowest frequency sinusoidal in the sum. In some contexts, the fundamental is usually abbreviated as ** f_{0}**, indicating the lowest frequency counting from zero. In other contexts, it is more common to abbreviate it as

Since the fundamental is the lowest frequency and is also perceived as the loudest, the ear identifies it as the specific pitch of the musical tone [harmonic spectrum]....The individual partials are not heard separately but are blended together by the ear into a single tone.

The **phase velocity** of a wave is the rate at which the phase of the wave propagates in space. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave will appear to travel at the phase velocity. The phase velocity is given in terms of the wavelength λ (lambda) and time period T as

In optics, the **refractive index** or **index of refraction** of a material is a dimensionless number that describes how fast light propagates through the material. It is defined as

In physics, the **wavelength** is the **spatial period** of a periodic wave—the distance over which the wave's shape repeats. It is thus the inverse of the spatial frequency. Wavelength is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. Wavelength is commonly designated by the Greek letter *lambda* (λ). The term *wavelength* is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.

In physics, a **wave** is a disturbance that transfers energy through matter or space, with little or no associated mass transport. Waves consist of oscillations or vibrations of a physical medium or a field, around relatively fixed locations. From the perspective of mathematics, waves, as functions of time and space, are a class of signals.

The **propagation constant** of a sinusoidal electromagnetic wave is a measure of the change undergone by the amplitude and phase of the wave as it propagates in a given direction. The quantity being measured can be the voltage, the current in a circuit, or a field vector such as electric field strength or flux density. The propagation constant itself measures the change per unit length, but it is otherwise dimensionless. In the context of two-port networks and their cascades, **propagation constant **measures the change undergone by the source quantity as it propagates from one port to the next.

In the physical sciences, the **wavenumber** 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 unit time, wavenumber is the number of waves per unit distance.

In optics, **dispersion** is the phenomenon in which the phase velocity of a wave depends on its frequency.

**Angular resolution** or **spatial resolution** describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object, thereby making it a major determinant of image resolution. In physics and geosciences, the term *spatial resolution* refers to the precision of a measurement with respect to space.

In radiometry, **irradiance** is the radiant flux (power) *received* by a *surface* per unit area. The SI unit of irradiance is the watt per square metre. The CGS unit erg per square centimetre per second is often used in astronomy. Irradiance is often called intensity because it has the same physical dimensions, but this term is avoided in radiometry where such usage leads to confusion with radiant intensity.

In physics, a **wave vector** is a vector which helps describe a wave. Like any vector, it has a magnitude and direction, both of which are important: Its magnitude is either the wavenumber or angular wavenumber of the wave, and its direction is ordinarily the direction of wave propagation.

In radiometry, **radiant intensity** is the radiant flux emitted, reflected, transmitted or received, per unit solid angle, and **spectral intensity** is the radiant intensity per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. These are *directional* quantities. The SI unit of radiant intensity is the watt per steradian, while that of spectral intensity in frequency is the watt per steradian per hertz and that of spectral intensity in wavelength is the watt per steradian per metre —commonly the watt per steradian per nanometre. Radiant intensity is distinct from irradiance and radiant exitance, which are often called *intensity* in branches of physics other than radiometry. In radio-frequency engineering, radiant intensity is sometimes called **radiation intensity**.

In physics, the **gyromagnetic ratio** of a particle or system is the ratio of its magnetic moment to its angular momentum, and it is often denoted by the symbol *γ*, gamma. Its SI unit is the radian per second per tesla (rad⋅s^{−1}⋅T^{−1}) or, equivalently, the coulomb per kilogram (C⋅kg^{−1}).

In fluid dynamics, **dispersion** of water waves generally refers to frequency dispersion, which means that waves of different wavelengths travel at different phase speeds. Water waves, in this context, are waves propagating on the water surface, with gravity and surface tension as the restoring forces. As a result, water with a free surface is generally considered to be a dispersive medium.

An **acousto-optic modulator (AOM)**, also called a **Bragg cell**, uses the acousto-optic effect to diffract and shift the frequency of light using sound waves. They are used in lasers for Q-switching, telecommunications for signal modulation, and in spectroscopy for frequency control. A piezoelectric transducer is attached to a material such as glass. An oscillating electric signal drives the transducer to vibrate, which creates sound waves in the material. These can be thought of as moving periodic planes of expansion and compression that change the index of refraction. Incoming light scatters off the resulting periodic index modulation and interference occurs similar to Bragg diffraction. The interaction can be thought of as a three-wave mixing process resulting in Sum-frequency generation or Difference-frequency generation between phonons and photons.

The **electromagnetic wave equation** is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric field **E** or the magnetic field **B**, takes the form:

**Photon energy** is the energy carried by a single photon. The amount of energy is directly proportional to the photon's electromagnetic frequency and inversely proportional to the wavelength. The higher the photon's frequency, the higher its energy. Equivalently, the longer the photon's wavelength, the lower its energy.

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