Frequency 10779 226090917 2008-07-16T19:58:58Z ClueBot 4928500 Reverting possible vandalism by [[Special:Contributions/96.229.199.186|96.229.199.186]] to older version. False positive? [[User:ClueBot/FalsePositives|Report it]]. Thanks, [[User:ClueBot]]. (441785) (Bot) {{Unreferenced|date=November 2007}} {{otheruses}} [[Image:Sine waves different frequencies.svg|thumb|right|360px|[[Sinusoidal wave]]s of various frequencies; the bottom waves have higher frequencies than those above. The horizontal axis represents time.]] '''Frequency''' is a [[measurement|measure]] of the number of occurrences of a repeating event per unit [[time]]. 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 (mathematics)|reciprocal]] of the frequency. == Definition and units == For [[cycle|cyclical]] processes, such as [[rotation]], [[oscillation]]s, or [[wave]]s, frequency is defined as a number of [[cycle]]s, or periods, 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 a Greek letter ''ν'' (nu). In [[SI derived unit|SI]] units, the unit of frequency is [[Hertz|hertz (Hz)]], named after the German physicist [[Heinrich Hertz]]. For example, 1 Hz means that an event repeats once per [[second]], 2 Hz is twice per second, and so on <ref>Accidentally, 1 [[hertz]] is the approximate frequency of a human heart (Herz in [[German language]])</ref>. This unit was originally called a [[cycle per second]] (cps), which is still sometimes used. [[Heart rate]] and musical [[tempo]] are measured in [[beats per minute]] (BPM). 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 [[hertz|Hz]]: thus, 60 BPM translates into 1 Hz. The period is usually denoted as ''T'', and is the [[reciprocal (mathematics)|reciprocal]] of the frequency ''f'': :<math> T = \frac{1}{f}. </math> The SI unit for period is the [[second|second (s)]]. == 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 [[bias (statistics)|biased]] underestimation of ''f'' by ½&nbsp;''f''&nbsp;/&nbsp;(''N''&nbsp;+&nbsp;½) in its [[expected value]]. 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: :<math> f = \frac{1}{T}. </math> 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 ''f<sub>0</sub>'', that must be tunable or very close to the measured frequency ''f''. Both the observed frequency and the reference frequency are simultaneously produced, and [[Beat (acoustics)|frequency beats]] are observed at a much lower frequency ''Δf'', which can be measured by counting. This is sometimes referred to as a [[stroboscope]] effect. The unknown frequency is then found from <math>f=f_0\pm \Delta f</math>. == Frequency of waves == <!-- This section is linked from [[Hearing impairment]] --> Frequency has an inverse relationship to the concept of [[wavelength]], simply, frequency is inversely proportional to wavelength ''λ'' (lambda). The frequency ''f'' is equal to the [[phase speed|speed]] ''v'' of the [[wave]] [[division (mathematics)|divided]] by the wavelength ''λ'' of the wave: :<math> f = \frac{v}{\lambda}. </math> In the [[special case]] of electromagnetic waves moving through a [[vacuum]], then ''v = c<sub>0</sub>'' , where ''c<sub>0</sub>'' is the [[speed of light]] in a vacuum, and this expression becomes: :<math> f = \frac{c_0}{\lambda}. </math> When [[waves]] from a [[monochrome|monochromatic]] source travel from one [[Medium (optics)|medium]] to another, their frequency remains exactly the same — only their [[wavelength]] and [[speed]] change. == Examples == * In [[music]] and [[acoustics]], the frequency of the [[note|standard pitch]] A above [[middle C]] on a [[piano]] is usually defined as [[A440|440 Hz]], that is, 440 cycles per second ({{Audio|Media-440Hz.ogg|Listen}}) and known as concert [[Pitch (music)|pitch]], to which an [[orchestra]] tunes. * 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 [[mains electricity|household electrical outlets]] is 50 Hz (close to the [[note|tone]] G), however, in [[North America]] and Northern [[South America]], the frequency of the [[alternating current]] is 60 Hz (between the [[note|tones]] B♭ and B — that is, a [[minor third]] above the European frequency). The frequency of the '[[mains hum|hum]]' in an [[audio recording]] can show where the recording was made — in countries utilizing the European, or the American grid frequency. *[[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 wave]]s, tend to be described by wave period rather than frequency. Short and fast waves, like [[Sound|audio]] and [[radio]], are usually described by their frequency instead of period. These commonly used conversions are listed below: {| class="wikitable" |- ! Frequency | 1 mHz (10<sup>-3</sup>) | 1 Hz (10<sup>0</sup>) | 1 kHz (10<sup>3</sup>) || 1 MHz (10<sup>6</sup>) | 1 GHz (10<sup>9</sup>) || 1 THz (10<sup>12</sup>) |- ! Period (time) | 1 ks (10<sup>3</sup>) | 1 s (10<sup>0</sup>) | 1 ms (10<sup>-3</sup>) || 1 µs (10<sup>-6</sup>) | 1 ns (10<sup>-9</sup>) || 1 ps (10<sup>-12</sup>) |} == Other types of frequency == *[[Angular frequency]] ''ω'' is defined as the rate of change in the orientation angle (during rotation), or in the [[phase (waves)|phase]] of a [[sinusoid]]al waveform (e.g. in oscillations and waves): ::<math>\omega=2\pi f\,</math>. :Angular frequency is measured in [[radian]]s per second (rad/s). *[[Spatial frequency]] is analogous to temporal frequency, but the time axis is replaced by one or more spatial displacement axes. *[[Wavenumber]] is the spatial analogue of angular frequency. In case of more than one space dimension, wavenumber is a [[vector]] quantity. == See also == {{portalpar|Electronics|Nuvola_apps_ksim.png}} * [[Negative frequency]] * [[Periodicity]] * [[Frequency converter]] * [[Frequency range]] or frequency band * [[Letter frequencies]] * [[Pitch (music)]] * [[Natural frequency]] == References == <references/> == External links == {{Wiktionarypar2|frequency|often}} * [http://inms-ienm.nrc-cnrc.gc.ca/research/optical_frequency_projects_e.html#femtosecond National Research Council of Canada: ''Femtosecond comb; The measurement of optical frequencies''] * [http://www.sengpielaudio.com/calculator-wavelength.htm Conversion: frequency to wavelength and back] * [http://www.sengpielaudio.com/calculator-period.htm Conversion: period, cycle duration, periodic time to frequency] * [http://www.sengpielaudio.com/calculator-notenames.htm Keyboard frequencies = naming of notes - The English and American system versus the German system] * [http://www.acoustics.salford.ac.uk/schools/index1.htm Teaching resource for 14-16yrs on sound including frequency] * [http://www.ikalogic.com/freq_meter.php A simple tutorial on how to build a frequency meter] * [http://www.diracdelta.co.uk/science/source/f/r/frequency/source.html Frequency - diracdelta.co.uk] - javascript calculation. 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