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{{dablink|For quantum-mechanical amplitude, see [[probability amplitude]]. For the video game of the same name, see [[Amplitude (video game)]]. Peak to Peak redirects here. For the school of that name, see [[Peak to Peak Charter School]]}}
{{Refimprove|date=October 2007}}

'''Amplitude''' is the [[magnitude (mathematics)|magnitude]] of change in the oscillating variable with each [[oscillation]] within an oscillating system. For example, [[sound waves]] in air are oscillations in [[atmospheric pressure]] and their amplitudes are proportional to the change in [[pressure]] during one oscillation. If a variable undergoes regular oscillations, and a graph of the system is drawn with the oscillating variable as the vertical axis and time as the horizontal axis, the amplitude is visually represented by the vertical distance between the [[extrema]] of the curve.

In older texts the [[Phase (waves)|phase]] is sometimes very confusingly called the amplitude.<ref>{{Cite book | author1=Knopp, Konrad| author2= Bagemihl, Frederick | authorlink1=Konrad Knopp | title=Theory of Functions Parts I and II | year=1996 | publisher=Dover Publications | isbn=0-486-69219-1 | page=3}}</ref>

==Concepts==
===Peak-to-peak amplitude===
Peak-to-peak amplitude is the change between peak (highest amplitude value) and trough (lowest amplitude value, which can be negative). With appropriate circuitry, peak-to-peak amplitudes can be measured by [[Meter (electronics)|meter]]s or by viewing the waveform on an [[oscilloscope]]. Peak-to-peak is a straightforward measurement on an oscilloscope, the peaks of the waveform being easily identified and measured against the [[Oscilloscope#Graticule|graticule]]. This remains a common way of specifying amplitude, but sometimes other measures of amplitude are more appropriate.

===Peak amplitude===
In [[audio system measurements]], [[telecommunications]] and other areas where the [[wikt:measurand|measurand]] is a signal that swings above and below a zero value but is not [[Sine wave|sinusoidal]], peak amplitude is often used. This is the [[absolute value]] of the signal.

===Semi-amplitude===
Semi-amplitude means half the peak-to-peak amplitude.<ref name="Tatum">Tatum, J. B. ''[http://orca.phys.uvic.ca/~tatum/celmechs/celm18.pdf Physics - Celestial Mechanics].'' Paragraph 18.2.12. 2007. Retrieved 2008-08-22.</ref> It is the most widely used measure of orbital amplitude in [[astronomy]] and the measurement of small semi-amplitudes of nearby stars is important in the search for [[exoplanet]]s.<ref>Uriel A. Goldvais. [http://img2.tapuz.co.il/forums/1_109580628.pdf Exoplanets], pp.2-3.</ref> For a sine wave, peak amplitude and semi-amplitude are the same.

Some scientists<ref>Regents of the [[University of California]]. ''[http://cse.ssl.berkeley.edu/light/measure_amp.html#measure4 Universe of Light: What is the Amplitude of a Wave?]'' 1996. Retrieved 2008-08-22</ref> use "amplitude" or "peak amplitude" to mean semi-amplitude, that is, half the peak-to-peak amplitude.<ref name="Tatum"/>

===Root mean square amplitude===
'''[[Root mean square]]''' ('''RMS''') '''amplitude''' is used especially in [[electrical engineering]]: the RMS is defined as the [[square root]] of the [[mean]] over time of the square of the vertical distance of the graph from the rest state.<ref>Department of Communicative Disorders [[University of Wisconsin–Madison]]. ''[http://www.comdis.wisc.edu/vcd202/rms.html RMS Amplitude]''. Retrieved 2008-08-22</ref>

For complex waveforms, especially non-repeating signals like noise, the RMS amplitude is usually used because it is both unambiguous and has physical significance. For example, the average [[power (physics)|power]] transmitted by an acoustic or [[electromagnetic wave]] or by an electrical signal is proportional to the square of the RMS amplitude (and not, in general, to the square of the peak amplitude).<ref>Ward, ''Electrical Engineering Science'', pp141-142, McGraw-Hill, 1971.</ref>

[[File:Sine voltage.svg|thumb|A [[Sine wave|sinusoidal]] curve 1 = Peak amplitude (<math>\scriptstyle\hat U</math>), 2 = [[#Peak-to-peak_amplitude|Peak-to-peak]] amplitude (<math>\scriptstyle2\hat U</math>), 3 = [[Root mean square|RMS]] amplitude (<math>\scriptstyle\hat U/\sqrt{2}</math>), 4 = [[Wave period]] (not an amplitude)]]

For [[alternating current]] [[electric power|electrical power]], the universal practice is to specify RMS values of a sinusoidal waveform. The peak-to-peak voltage of a sine wave is nearly 3 times the RMS value, but is rarely used. Some common [[voltmeter|meter types]] used in electrical engineering are calibrated for RMS amplitude, but actually operate on a DC input. Both digital voltmeters and moving coil meters are in this category. Such meters require the AC input to be first [[rectifier|rectified]]. They are not true RMS meters, but rather, are reading proportional to either rectified average or peak amplitude. The RMS calibration is only correct for a sine wave input since the ratio between peak, average and RMS values is dependent on [[waveform]]. Until recently, true RMS meters were mostly used only in [[radio frequency]] measurements. These instruments based their measurement on detecting the heating effect in a load resistor with a [[thermistor]]. The advent of [[microprocessor]] controlled meters capable of calculating RMS by [[Sampling (signal processing)|sampling]] the waveform has made true RMS measurement commonplace.

===Ambiguity===
In general, the use of peak amplitude is simple and unambiguous only for symmetric periodic waves, like a [[sine]] wave, a [[square wave]], or a triangular wave. For an asymmetric wave (periodic pulses in one direction, for example), the peak amplitude becomes ambiguous. This is because the value is different depending on whether the maximum positive signal is measured relative to the mean, the maximum negative signal is measured relative to the mean, or the maximum positive signal is measured relative to the maximum negative signal (the '''peak-to-peak amplitude''') and then divided by two. In electrical engineering, the usual solution to this ambiguity is to measure the amplitude from a defined reference potential (such as [[Ground (electricity)|ground]] or 0 V). Strictly speaking, this is no longer amplitude since there is the possibility that a constant (DC component) is included in the measurement.

===Pulse amplitude===
In [[telecommunication]], ''pulse amplitude'' is the magnitude of a [[pulse (signal processing)|pulse]] parameter, such as the [[voltage]] level, [[Electric current|current]] level, [[field intensity]], or [[Power (physics)|power]] level.

Pulse amplitude is measured with respect to a specified reference and therefore should be modified by qualifiers, such as "average", "instantaneous", "peak", or "[[root mean square|root-mean-square]]".

Pulse amplitude also applies to the amplitude of [[frequency]]- and [[phase (waves)|phase]]-modulated [[waveform]] envelopes.<ref>{{FS1037C}}</ref>

==Formal representation==
In this simple [[wave equation]]
:<math>
x = A \sin(t - K) + b \ ,
</math>

''A'' is the peak amplitude of the wave, 
''x'' is the oscillating variable, 
''t'' is time, 
''K'' and ''b'' are arbitrary constants representing time and displacement offsets respectively.

The units of the amplitude depend on the type of wave, but are always in the same units as the oscillating variable. A more general representation of the wave equation is more complex, but the role of amplitude remains analogous to this simple case.

For waves on a [[vibrating string|string]], or in medium such as [[water]], the amplitude is a [[Displacement (vector)|displacement]].

The amplitude of sound waves and audio signals (which relates to the volume) conventionally refers to the amplitude of the [[Sound#Sound pressure|air pressure]] in the wave, but sometimes the amplitude of the [[Particle displacement|displacement]] (movements of the air or the diaphragm of a [[loudspeaker|speaker]]) is described. The [[logarithm]] of the amplitude squared is usually quoted in [[decibel|dB]], so a null amplitude corresponds to −[[infinity|∞]] dB. [[Loudness]] is related to amplitude and [[Sound intensity|intensity]] and is one of most salient qualities of a sound, although in general sounds can be recognized [[Amplitude scaling invariance|independently of amplitude]]. The square of the amplitude is proportional to the [[Sound intensity|intensity]] of the wave.

For [[electromagnetic radiation]], the amplitude of a photon corresponds to the changes in the [[electric field]] of the wave. However radio signals may be carried by electromagnetic radiation; the intensity of the radiation ([[amplitude modulation]]) or the frequency of the radiation ([[frequency modulation]]) is oscillated and then the individual oscillations are varied (modulated) to produce the signal.

==Waveform and envelope==
The amplitude may be constant (in which case the wave is a [[continuous wave]]) or may vary with time and/or position. The form of the variation of amplitude is called the [[envelope detector|envelope]] of the wave.

If the [[waveform]] is a pure [[sine wave]], the relationships between peak-to-peak, peak, mean, and [[Root mean square|RMS]] amplitudes are fixed and known, as they are for any continuous [[Period (physics)|periodic]] wave. However, this is not true for an arbitrary waveform which may or may not be periodic or continuous.

For a [[sine wave]] the relationship between RMS and peak-to-peak amplitude is:
:<math>
\mbox{Peak-to-peak} = 2 \sqrt{2} \times \mbox{RMS} \approx 2.8 \times \mbox{RMS} \,
</math>.

For other waveforms the relationships are not (necessarily) arithmetically the same as they are for sine waves.

==See also==
{{wiktionary|amplitude}}
*[[Wave]]s and their properties:
**[[Frequency]]
**[[Period (physics)|Period]]
**[[Wavelength]]
**[[Crest factor]]
*[[Amplitude modulation]]

==Notes==
{{Reflist}}

[[Category:Physical quantities]]
[[Category:Sound]]
[[Category:Fundamental physics concepts]]

[[ar:مطال]]
[[bg:Амплитуда]]
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[[th:แอมพลิจูด]]
[[tr:Genlik]]
[[uk:Амплітуда]]
[[ur:حیطہ (طبیعیات)]]
[[vi:Biên độ]]
[[zh:振幅]]

Amplitude - Revision history

Admin: Created page with "{{dablink|For quantum-mechanical amplitude, see probability amplitude. For the video game of the same name, see Amplitude (video game). Peak to Peak redirects here. For t..."