1 Definitions 2 Units 3 Period versus frequency 4 Related types of frequency 5 In wave propagation 6 Measurement
7.1 Light 7.2 Sound 7.3 Line current
8 See also 9 Notes and references 10 Further reading 11 External links
These three dots are flashing, or cycling, periodically—from lowest frequency (0.5 hertz) to highest frequency (2.0 hertz), top to bottom. For each flashing dot: "f" is the frequency in hertz, (Hz)—or the number of events per second (cycles per second)—that the dot flashes; while "T" is the period, or time, in seconds (s) of each cycle, (the number of seconds per cycle). Note T and f are reciprocal values to each other.
As time elapses—here moving left to right on the horizontal axis—the five sinusoidal waves vary, or cycle, regularly at different rates. The red wave (top) has the lowest frequency (cycles at the slowest rate) while the purple wave (bottom) has the highest frequency (cycles at the fastest rate).
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). The relation between the frequency and the period
of a repeating event or oscillation is given by
displaystyle f= frac 1 T .
SI derived unit
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)
Related types of frequency
For other uses, see
Diagram of the relationship between the different types of frequency and other wave properties.
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
f t )
displaystyle y(t)=sin left(theta (t)right)=sin(omega t)=sin(2mathrm pi ft)
= ω = 2
displaystyle frac mathrm d theta mathrm d t =omega =2mathrm 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 sample time, which is a dimensionless quantity. Angular frequency (in radians) is larger than regular frequency (in Hz) by a factor of 2π.
y ( t ) = sin
θ ( t , x )
= sin ( ω t + k x )
displaystyle y(t)=sin left(theta (t,x)right)=sin(omega t+kx)
displaystyle frac mathrm d theta mathrm d x =k
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.
In wave propagation 
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:
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
displaystyle f= frac 71 15, text s approx 4.7, 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 Δf = 1/(2 Tm), or a fractional error of Δf / f = 1/(2 f Tm) where Tm 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.
A resonant-reed frequency meter, an obsolete device used from about 1900 to the 1940s for measuring the frequency of alternating current. It consists of a strip of metal with reeds of graduated lengths, vibrated by an electromagnet. When the unknown frequency is applied to the electromagnet, the reed which is resonant at that frequency will vibrate with large amplitude, visible next to the scale.
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.
Modern 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.
Complete spectrum of electromagnetic radiation with the visible portion highlighted
Visible light is an electromagnetic wave, consisting of oscillating electric and magnetic fields traveling through space. The frequency of the wave determines its color: 7014400000000000000♠4×1014 Hz is red light, 7014800000000000000♠8×1014 Hz is violet light, and between these (in the range 4-7014800000000000000♠8×1014 Hz) are all the other colors of the visible spectrum. An electromagnetic wave can have a frequency less than 7014400000000000000♠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 7014800000000000000♠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 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.
c = f λ
displaystyle displaystyle c=flambda
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
Main article: Audio frequency
Bandwidth (signal processing)
Notes and references
^ "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.
^ "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). "
Giancoli, D.C. (1988).
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 14-16yrs on sound including frequency
A simple tutorial on how to build a frequency meter
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