Sinusoidal waves of various frequencies; the bottom waves have higher frequencies than those above. The horizontal axis represents time.

Frequency is a measure of the number of occurrences of a repeating event per unit time. Measurement is the process of estimating the magnitude of some attribute of an object such as its length or weight relative to some standard ( unit of measurement) such as For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of It is also referred to as temporal frequency. The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency. A tone may be sustained for varying lengths of time. duration is a property of tone that becomes one of the bases rhythem or an amount of Time or a particular time In Mathematics, a multiplicative inverse for a number x, denoted by 1&frasl x or x &minus1 is a number which

## Definition and units

For cyclical processes, such as rotation, oscillations, or waves, frequency is defined as a number of cycles, or periods, per unit time. A rotation is a movement of an object in a circular motion A two- Dimensional object rotates around a center (or point) of rotation Oscillation is the repetitive variation typically in Time, of some measure about a central value (often a point of Equilibrium) or between two or more different states A wave is a disturbance that propagates through Space and Time, usually with transference of Energy. In physics and engineering disciplines, such as optics, acoustics, and radio, frequency is usually denoted by a Latin letter f or by a Greek letter ν (nu). Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Engineering is the Discipline and Profession of applying technical and scientific Knowledge and Acoustics is the interdisciplinary science that deals with the study of Sound, Ultrasound and Infrasound (all mechanical waves in gases liquids and solids Radio is the transmission of signals by Modulation of electromagnetic waves with frequencies below those of visible Light.

In SI units, the unit of frequency is hertz (Hz), named after the German physicist Heinrich Hertz. SI derived units are part of the SI system of measurement units and are derived from the seven SI base units They are derived from SI basic units/defined The hertz (symbol Hz) is a measure of Frequency, informally defined as the number of events occurring per Second. Heinrich Rudolf Hertz ( February 22, 1857 – January 1, 1894) was a German physicist who clarified and expanded the electromagnetic theory For example, 1 Hz means that an event repeats once per second, 2 Hz is twice per second, and so on [1]. The second ( SI symbol s) sometimes abbreviated sec, is the name of a unit of Time, and is the International System of Units This unit was originally called a cycle per second (cps), which is still sometimes used. The cycle per second was a once-common unit of Frequency. With the organisation of the International System of Units (abbreviated SI from the French in Heart rate and musical tempo are measured in beats per minute (BPM). Measuring heart rate The Pulse rate (which in most people is identical to the heart rate can be measured at any point on the body where an Artery 's pulsation 2266-Tetramethylpiperidine-1-oxyl or TEMPO is the Chemical compound with the formula (CH23(CMe22NO Beats per minute ( BPM) is a unit typically used as either a measure of Tempo in music or a measure of one's Heart rate. Frequency of rotation is often expressed as a number of revolutions per minute (rpm). BPM and rpm values must be divided by 60 to obtain the corresponding value in Hz: thus, 60 BPM translates into 1 Hz. The hertz (symbol Hz) is a measure of Frequency, informally defined as the number of events occurring per Second.

The period is usually denoted as T, and is the reciprocal of the frequency f:

$T = \frac{1}{f}.$

The SI unit for period is the second (s). In Mathematics, a multiplicative inverse for a number x, denoted by 1&frasl x or x &minus1 is a number which The second ( SI symbol s) sometimes abbreviated sec, is the name of a unit of Time, and is the International System of Units

## Measurement

### By timing

To calculate the frequency of an event, the number of occurrences of the event within a fixed time interval are counted, and then divided by the length of the time interval.

In experimental work (for example, calculating the frequency of an oscillating pendulum) it is more accurate to measure the time taken for a fixed number of occurrences, rather than the number of occurrences within a fixed time. The latter method introduces — if N is the number of counted occurrences — a random error between zero and one count, so on average half a count, causing an biased underestimation of f by ½ f / (N + ½) in its expected value. In Statistics and optimization, the concepts of statistical error and residual are easily confused with each other In Mathematics, an average, or central tendency of a Data set refers to a measure of the "middle" or " expected " value of In the first method, which is more accurate, frequency is still calculated by dividing the number of occurrences by the time interval; however it is the number of occurrences that is fixed, not the time interval.

An alternative method to calculate frequency is to measure the time between two consecutive occurrences of the event (the period T) and then compute the frequency f as the reciprocal of this time:

$f = \frac{1}{T}.$

A more accurate measurement can be obtained by taking many cycles into account and averaging the periods between each.

### By stroboscope effect, or frequency beats

In case when the frequency is so high that counting is difficult or impossible with the available means, another method is used, based on a source (such as a laser, a tuning fork, or a waveform generator) of a known reference frequency f0, that must be tunable or very close to the measured frequency f. A laser is a device that emits Light ( Electromagnetic radiation) through a process called Stimulated emission. A tuning fork is an acoustic Resonator in the form of a two-pronged Fork with the tines formed from a U-shaped bar of elastic A signal generator, also known variously as a test signal generator, function generator, tone generator, arbitrary waveform generator, digital Both the observed frequency and the reference frequency are simultaneously produced, and frequency beats are observed at a much lower frequency Δf, which can be measured by counting. In Acoustics, a beat is an Interference between two Sounds of slightly different frequencies, perceived as periodic variations in volume whose This is sometimes referred to as a stroboscope effect. A stroboscope, also known as a strobe, is an instrument used to make a cyclically moving object appear to be slow-moving or stationary The unknown frequency is then found from $f=f_0\pm \Delta f$.

## Frequency of waves

Frequency has an inverse relationship to the concept of wavelength, simply, frequency is inversely proportional to wavelength λ (lambda). In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. The frequency f is equal to the speed v of the wave divided by the wavelength λ of the wave:

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

In the special case of electromagnetic waves moving through a vacuum, then v = c0 , where c0 is the speed of light in a vacuum, and this expression becomes:

$f = \frac{c_0}{\lambda}.$

When waves from a monochromatic source travel from one medium to another, their frequency remains exactly the same — only their wavelength and speed change. The phase velocity (or phase speed) of a Wave is the rate at which the phase of the wave propagates in space A wave is a disturbance that propagates through Space and Time, usually with transference of Energy. In Mathematics, especially in elementary Arithmetic, division is an arithmetic operation which is the inverse of Multiplication. In Logic, especially as applied in Mathematics, concept A is a special case or Specialization of concept B precisely if every instance of A is also This vacuum means "absence of matter" or "an empty area or space" for the cleaning appliance see Vacuum cleaner. A wave is a disturbance that propagates through Space and Time, usually with transference of Energy. Monochrome comes from the Greek μονόχρωμος ( monochromos) meaning “of one color” which is a combination An optical medium is material through which Electromagnetic waves propagate In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. Speed is the rate of motion, or equivalently the rate of change in position often expressed as Distance d traveled per unit of

## Examples

• In music and acoustics, the frequency of the standard pitch A above middle C on a piano is usually defined as 440 Hz, that is, 440 cycles per second (Listen ) and known as concert pitch, to which an orchestra tunes. Music is an Art form in which the medium is Sound organized in Time. Acoustics is the interdisciplinary science that deals with the study of Sound, Ultrasound and Infrasound (all mechanical waves in gases liquids and solids In Music, the term note has two primary meanings 1 a sign used in Musical notation to represent the relative duration and pitch of a Sound; C or Do is the first Note of the fixed-Do Solfege. In Western Music, the expression " Middle C " refers to the note The piano is a Musical instrument played by means of a keyboard that produces sound by striking steel strings with Felt covered hammers A440 is the 440 Hz tone that serves as the standard for musical pitch. Pitch represents the perceived Fundamental frequency of a sound An orchestra is an instrumental ensemble, usually fairly large with string brass woodwind sections and possibly a percussion section as well
• A baby can hear tones with oscillations up to approximately 20,000 Hz, but these frequencies become more difficult to hear as people age.
• In Europe, Africa, Australia, Southern South America, most of Asia, and in Russia, the frequency of the alternating current in household electrical outlets is 50 Hz (close to the tone G), however, in North America and Northern South America, the frequency of the alternating current is 60 Hz (between the tones B♭ and B — that is, a minor third above the European frequency). For a topic outline on this subject see List of basic Australia topics. South America is a Continent of the Americas, situated entirely in the Western Hemisphere and mostly in the Southern Hemisphere, with a Russia (Россия Rossiya) or the Russian Federation ( Rossiyskaya Federatsiya) is a transcontinental Country extending An alternating current ( AC) is an Electric current whose direction reverses cyclically as opposed to Direct current, whose direction remains constant Mains is the general-purpose Alternating current (AC Electric power supply (as in "I've connected the appliance to the mains" In Music, the term note has two primary meanings 1 a sign used in Musical notation to represent the relative duration and pitch of a Sound; South America is a Continent of the Americas, situated entirely in the Western Hemisphere and mostly in the Southern Hemisphere, with a An alternating current ( AC) is an Electric current whose direction reverses cyclically as opposed to Direct current, whose direction remains constant In Music, the term note has two primary meanings 1 a sign used in Musical notation to represent the relative duration and pitch of a Sound; A minor third ( is the smaller of two commonly occurring musical intervals compounded of two steps of the Diatonic scale. The frequency of the 'hum' in an audio recording can show where the recording was made — in countries utilizing the European, or the American grid frequency. Electric hum, Mains hum, or power line hum is an audible oscillation at the frequency of the Mains Alternating current
• Visible light from deep red to violet has frequencies of 430 to 750 THz.

## Period versus frequency

As a matter of convenience, longer and slower waves, such as ocean surface waves, tend to be described by wave period rather than frequency. Ocean surface waves are Surface waves that occur on the Free surface of the Ocean. Short and fast waves, like audio and radio, are usually described by their frequency instead of period. Sound' is Vibration transmitted through a Solid, Liquid, or Gas; particularly sound means those vibrations composed of Frequencies Radio is the transmission of signals by Modulation of electromagnetic waves with frequencies below those of visible Light. These commonly used conversions are listed below:

 Frequency Period (time) 1 mHz (10-3) 1 Hz (100) 1 kHz (103) 1 MHz (106) 1 GHz (109) 1 THz (1012) 1 ks (103) 1 s (100) 1 ms (10-3) 1 µs (10-6) 1 ns (10-9) 1 ps (10-12)

## Other types of frequency

• Angular frequency ω is defined as the rate of change in the orientation angle (during rotation), or in the phase of a sinusoidal waveform (e. Do not confuse with Angular velocity In Physics (specifically Mechanics and Electrical engineering) angular frequency The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0 g. in oscillations and waves):
$\omega=2\pi f\,$.
Angular frequency is measured in radians per second (rad/s). The radian is a unit of plane Angle, equal to 180/ π degrees, or about 57
• Spatial frequency is analogous to temporal frequency, but the time axis is replaced by one or more spatial displacement axes. In Mathematics, Physics, and Engineering, spatial frequency is a characteristic of any structure that is periodic across position in space
• Wavenumber is the spatial analogue of angular frequency. Wavenumber in most physical sciences is a Wave property inversely related to Wavelength, having SI units of reciprocal meters In case of more than one space dimension, wavenumber is a vector quantity.