Open Access Articles Top Results for Frequency
International Journal of Innovative Research in Science, Engineering and Technology
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Load Frequency Control of MultiArea Power Systems Using PI, PID, and Fuzzy Logic Controlling TechniquesFrequency
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frequency  

Common symbols  f, ν 
SI unit  hertz 
In SI base units  s^{−1} 
Frequency is the number of occurrences of a repeating event per unit time.^{[1]} It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency. The period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency.^{[2]} For example, if a newborn baby's heart beats at a frequency of 120 times a minute, its period – the interval between beats – is half a second (60 seconds (i.e. a minute) 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 (sound) signals, radio waves, and light.
Contents
Definitions and units
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 (nu). Note, the related concept, angular frequency, is usually denoted by the Greek letter ω (omega), which uses the SI unit radians per second (rad/s).
For counts per unit of time, the SI unit for frequency is hertz (Hz), named after the German physicist Heinrich Hertz; 1 Hz means that an event repeats once per second. A previous name for this unit was cycles per second (cps).
A traditional unit of measure used with rotating mechanical devices is revolutions per minute, abbreviated r/min or rpm. 60 r/min equals one hertz.^{[3]}
The period, usually denoted by T, is the duration of one cycle, and is the reciprocal of the frequency f:
 <math>T = \frac{1}{f}.</math>
The SI unit for period is the second.
Other than waves frequency related to occurrence of something can be denoted by:
<math>f = \frac{n}{t}</math>
Where <math>n </math> is the number of times an event occurred and <math>t</math> is the duration.
Frequency may also be denoted by the lowercase letter Nu, <math>\nu</math> (see e.g. Planck's formula).
Measurement
By 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 length of the time period. For example, if 71 events occur within 15 seconds the frequency is:
 <math>f = \frac{71}{15 \,\text{s}} \approx 4.7 \, \text{Hz}</math>
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 Δf = 1/(2 T_{m}), or a fractional error of Δf / f = 1/(2 f T_{m}) where T_{m} is the timing interval and f is the measured frequency. This error decreases with frequency, so it is a problem at low frequencies where the number of counts N is small.
By stroboscope
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 integer multiple of the strobing frequency will also appear stationary.
By frequency counter
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. Frequency counters can currently 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.
Heterodyne 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, which must be determined by some other method. 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).
Frequency of waves
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:
 <math>
f = \frac{v}{\lambda}. </math>
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:
 <math>
f = \frac{c}{\lambda}. </math>
When waves from a monochrome source travel from one medium to another, their frequency remains the same—only their wavelength and speed change.
Examples
Light
Visible light is an electromagnetic wave, consisting of oscillating electric and magnetic fields traveling through space. The frequency of the wave determines its color: 4×10^{14} Hz is red light, 8×10^{14}Lua error: Unmatched closebracket at pattern character 67. is violet light, and between these (in the range 48×10^{14}Lua error: Unmatched closebracket at pattern character 67.) are all the other colors of the rainbow. An electromagnetic wave can have a frequency less than 4×10^{14}Lua error: Unmatched closebracket at pattern character 67., 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 8×10^{14}Lua error: Unmatched closebracket at pattern character 67., but it will be invisible to the human eye; such waves are called ultraviolet (UV) radiation. Even higherfrequency waves are called Xrays, and higher still are gamma rays.
All of these waves, from the lowestfrequency radio waves to the highestfrequency 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.
 <math>\displaystyle c=f\lambda</math>
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
Sound propagates as mechanical vibration waves of pressure and displacement, in air or other substances.^{[5]} Frequency is the property of sound 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.
Line current
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.
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. 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})  1 Hz (10^{0})  1 kHz (10^{3})  1 MHz (10^{6})  1 GHz (10^{9})  1 THz (10^{12}) 

Period (time)  1 ks (10^{3})  1 s (10^{0})  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 of angular displacement, θ, (during rotation), or the rate of change of the phase of a sinusoidal waveform (e.g. in oscillations and waves), or as the rate of change of the argument to the sine function:
 <math>y(t) = \sin\left( \theta(t) \right) = \sin(\omega t) = \sin(2 \mathrm{\pi} f t)</math>
 <math>\frac{\mathrm{d} \theta}{\mathrm{d} t} = \omega = 2 \mathrm{\pi} f</math>
 Angular frequency is commonly measured in radians per second (rad/s) but, for discretetime signals, can also be expressed as radians per sample time, which is a dimensionless quantity.
 Spatial frequency is analogous to temporal frequency, but the time axis is replaced by one or more spatial displacement axes. E.g.:
 <math>y(t) = \sin\left( \theta(t,x) \right) = \sin(\omega t + kx)</math>
 <math>\frac{\mathrm{d} \theta}{\mathrm{d} x} = k</math>
 Wavenumber, k, sometimes means the spatial frequency analogue of angular temporal frequency. In case of more than one spatial dimension, wavenumber is a vector quantity.
Frequency ranges
The frequency range of a system is the range over which it is considered to provide a useful level of signal with acceptable distortion characteristics. A listing of the upper and lower limits of frequency limits for a system is not useful without a criterion for what the range represents.
Many systems are characterized by the range of frequencies to which they respond. Musical instruments produce different ranges of notes within the hearing range. The electromagnetic spectrum can be divided into many different ranges such as visible light, infrared or ultraviolet radiation, radio waves, Xrays and so on, and each of these ranges can in turn be divided into smaller ranges. A radio communications signal must occupy a range of frequencies carrying most of its energy, called its bandwidth. Allocation of radio frequency ranges to different uses is a major function of radio spectrum allocation.
See also
This "see also" section may contain an excessive number of suggestions. Please ensure that only the most relevant suggestions are given and that they are not red links, and consider integrating suggestions into the article itself. (September 2014)</small> 
It has been suggested that portions of this article be moved into Frequency (disambiguation). (Discuss) 
 Absolute threshold of hearing
 Audible range
 Bandwidth extension
 Bass (sound)
 Coherence bandwidth
 Critical band
 Cumulative frequency analysis
 Cutoff frequency
 Downsampling
 Electronic filter
 Flashes Per Minute
 Frequency converter
 Frequency domain
 Frequency distribution
 Frequency extender
 Frequency grid
 Free spectral range
 Frequency deviation
 Frequency spectrum
 Interaction frequency
 Musical acoustics
 MVDDS dispute
 Natural frequency
 Negative frequency
 Normalized frequency
 Passband
 Periodicity (disambiguation)
 Piano key frequencies
 Pink noise
 Preselector
 Power bandwidth
 Range (music)
 Radar signal characteristics
 Radio window
 Scientific pitch notation
 Signaling (telecommunications)
 Spectral width
 Spread spectrum
 Spectral component
 Spectrum allocation
 Symbol rate
 Transition band
 Transverter
 Ultrasound
 Upsampling
 Whistle register
 Wideband audio
References
 ^ http://www.merriamwebster.com/dictionary/frequency
 ^ http://www.merriamwebster.com/dictionary/period
 ^ Davies, A. (1997). Handbook of Condition Monitoring: Techniques and Methodology. New York: Springer. ISBN 9780412613203.
 ^ Bakshi, K.A.; A.V. Bakshi; U.A. Bakshi (2008). Electronic Measurement Systems. US: Technical Publications. pp. 4–14. ISBN 9788184312065.
 ^ http://www.merriamwebster.com/dictionary/sound
 ^ 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 20081022.
Further reading
 Giancoli, D.C. (1988). Physics for Scientists and Engineers (2nd ed.). Prentice Hall. ISBN 013669201X.
External links
40x40px  Look up frequency or often in Wiktionary, the free dictionary. 
 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 1416yrs on sound including frequency
 A simple tutorial on how to build a frequency meter
 Frequency  diracdelta.co.uk – JavaScript calculation.
