Editing Amplitude (section)

==Definitions==
[[File:Sine voltage.svg|thumb|A [[sine wave|sinusoidal]] curve
{{ordered list|
| list_style=list-style-position:inside; margin:0;
| Peak amplitude (<math>\scriptstyle\hat u</math>),
| Peak-to-peak amplitude (<math>\scriptstyle2\hat u</math>),
| Root mean square amplitude (<math>\scriptstyle\hat u/\sqrt{2}</math>),
| [[Wave period]] (not an amplitude)
}}]]

===Peak amplitude and semi-amplitude===
For symmetric periodic waves, like [[sine wave]]s or [[triangle wave]]s, ''peak amplitude'' and ''semi amplitude'' are the same.

====Peak amplitude====
{{anchor|Peak amplitude}}In [[audio system measurements]], [[telecommunications]] and others where the [[wikt:measurand|measurand]] is a signal that swings above and below a reference value but is not [[Sine wave|sinusoidal]], peak amplitude is often used. If the reference is zero, this is the maximum [[absolute value]] of the signal; if the reference is a mean value ([[DC component]]), the peak amplitude is the maximum absolute value of the difference from that reference.

====Semi-amplitude====
{{anchor|Semi-amplitude}}<!-- This section is the target of [[Semi-amplitude]].-->Semi-amplitude means half of the peak-to-peak amplitude.<ref name="Tatum">Tatum, J. B. ''[http://orca.phys.uvic.ca/~tatum/celmechs/celm18.pdf Physics &nbsp;– Celestial Mechanics].'' Paragraph 18.2.12. 2007. Retrieved 2008-08-22.</ref> 
The majority of scientific literature<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> employs the term ''amplitude'' or ''peak amplitude'' to mean semi-amplitude.

It is the most widely used measure of orbital wobble in [[astronomy]] and the measurement of small [[radial velocity]] semi-amplitudes of nearby stars is important in the search for [[exoplanet]]s (see [[Doppler spectroscopy]]).<ref>Goldvais, Uriel A. [http://img2.tapuz.co.il/forums/1_109580628.pdf Exoplanets] {{Webarchive|url=https://web.archive.org/web/20210303160140/http://img2.tapuz.co.il/forums/1_109580628.pdf |date=2021-03-03 }}, pp. 2–3. Retrieved 2008-08-22.</ref>

====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 triangle 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 (the ''semi-amplitude''). 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&nbsp;V). Strictly speaking, this is no longer amplitude since there is the possibility that a constant ([[DC component]]) is included in the measurement.

===Peak-to-peak amplitude{{anchor|Peak-to-peak}}=== 
'''Peak-to-peak amplitude''' (abbreviated '''p–p''' or '''PtP''' or '''PtoP''') is the change between peak (highest amplitude value) and [[Crest and trough|trough]] (lowest amplitude value, which can be negative). With appropriate circuitry, peak-to-peak amplitudes of electric oscillations can be measured by meters 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.

===Root mean square amplitude===
{{Further|Root mean square#In common waveforms{{!}}RMS of common waveforms}}

[[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] {{Webarchive|url=https://web.archive.org/web/20130911063155/http://www.comdis.wisc.edu/vcd202/rms.html |date=2013-09-11 }}''. Retrieved 2008-08-22.</ref>
i.e. the RMS of the AC waveform (with no [[DC component]]).

For complicated 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'', pp. 141–142, McGraw-Hill, 1971.</ref>

For [[alternating current]] [[electric power]], the  universal practice is to specify RMS values of a sinusoidal waveform. One property of root mean square voltages and currents is that they produce the same heating effect as a [[direct current]] in a given resistance.

The peak-to-peak value is used, for example, when choosing rectifiers for power supplies, or when estimating the maximum voltage that insulation must withstand. Some common [[voltmeter]]s are calibrated for RMS amplitude, but respond to the average value of a rectified waveform. Many digital voltmeters and all moving coil meters are in this category. The RMS calibration is only correct for a sine wave input since the ratio between peak, average and RMS values is dependent on [[waveform]]. If the wave shape being measured is greatly different from a sine wave, the relationship between RMS and average value changes. True RMS-responding meters were used in [[radio frequency]] measurements, where instruments measured the heating effect in a resistor to measure a current. The advent of [[microprocessor]]-controlled meters capable of calculating RMS by [[Sampling (signal processing)|sampling]] the waveform has made true RMS measurement commonplace.

===Pulse amplitude===
In telecommunications, ''pulse amplitude'' is the [[Magnitude (mathematics)|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''.

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