# Amplitude: Wikis

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# Encyclopedia

Amplitude is the magnitude of change in the oscillating variable, with each oscillation, within an oscillating system. For instance, sound waves are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation. If the 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 is sometimes very confusingly called the amplitude.[1]

## Concepts

### Peak-to-peak amplitude

Peak-to-peak amplitude is the measure of the change between peak (highest amplitude value) and trough (lowest amplitude value, which can be negative). Peak-to-peak amplitudes can be measured by meters with appropriate circuitry, or by viewing the waveform on an oscilloscope. Peak-to-peak is a straightforward measurement to make on an oscilloscope, the peaks of the waveform being easily identified and measured against the graticule. It 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 measurand is a signal that swings above and below a zero value but is not sinusoidal, peak amplitude is often used. This is the absolute value of the signal.

### Semi-amplitude

Semi-amplitude in fields such as astronomy is understood to mean half the peak-to-peak amplitude[2] and is important in the search for exoplanets.[3] For a sine wave, peak amplitude and semi-amplitude are the same.

Some scientists[4] use "amplitude" or "peak amplitude" to mean semi-amplitude, that is, half the peak-to-peak amplitude.[2]

### 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.[5]

For complex waveforms, especially non-repeating signals like noise, the RMS amplitude is usually used because it is unambiguous and because it has physical significance. For example, the average 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).[6]

A sinusoidal curve
1 = Peak amplitude ($\scriptstyle\hat U$),
2 = Peak-to-peak amplitude ($\scriptstyle2\hat U$),
3 = RMS amplitude ($\scriptstyle\hat U/\sqrt{2}$),
4 = Wave period (not an amplitude)

When dealing with alternating current electrical power it is universal 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 a rarely used measure in this field. Some common meter types used in electrical engineering are calibrated for RMS amplitude, but actually operate on a DC input. Digital voltmeters and moving coil meters are both in this category. Such meters require the AC input to be first rectified and are really reading proportional to either rectified average or peak amplitude. They are not true RMS meters and the RMS calibration is only correct for a sine wave input since the ratio between peak, average and rms values is dependant on waveform. True RMS meters do exist but until recently have been considered more specialised equipment; the advent of microprocessor controlled meters has made them more common.

### Ambiguity

The use of peak amplitude is simple and unambiguous 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 because the value obtained 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 or 0V). 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 parameter, such as the voltage level, current level, field intensity, or 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-modulated waveform envelopes.[7]

## Formal representation

In this simple wave equation

$x = A \sin(t - K) + b \ ,$

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 string, or in medium such as water, the amplitude is a displacement.

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

If the waveform is a pure sine wave, the relationships between peak-to-peak, peak, mean, and RMS amplitudes are fixed and known, as they are for any continuous 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:

$\mbox{Peak-to-peak} = 2 \sqrt{2} \times \mbox{RMS} \approx 2.8 \times \mbox{RMS} \,$.

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

## Notes

1. ^ Knopp, Konrad; Bagemihl, Frederick (1996). Theory of Functions Parts I and II. Dover Publications. p. 3. ISBN 0-486-69219-1.
2. ^ a b Tatum, J. B. Physics - Celestial Mechanics. Paragraph 18.2.12. 2007. Retrieved 2008-08-22.
3. ^ Uriel A. Goldvais. Exoplanets, pp.2-3.
4. ^ Regents of the University of California. Universe of Light: What is the Amplitude of a Wave? 1996. Retrieved 2008-08-22
5. ^ Department of Communicative Disorders University of Wisconsin–Madison. RMS Amplitude. Retrieved 2008-08-22
6. ^ Ward, Electrical Engineering Science, pp141-142, McGraw-Hill, 1971.
7. ^  This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C".

# 1911 encyclopedia

Up to date as of January 14, 2010

### From LoveToKnow 1911

AMPLITUDE (from Lat. amplus, large), in astronomy, the angular distance of the rising or setting sun, or other heavenly body, from the east or west point of the horizon; used mostly by navigators in finding the variation of the compass by the setting sun. In algebra, if a be a real positive quantity and w a root of unity, then a is the amplitude of the product aw. In elliptic integrals, the amplitude is the limit of integration when the integral is expressed in the form f 4) 1% I - N 2 sin e 4) d4. The hyperbolic or Gudermannian amplitude of the quantity x is ta n (sinh x). In mechanics, the amplitude of a wave is the maximum ordinate.

(See WAVE.)

# Wiktionary

Up to date as of January 15, 2010

## German

### Noun

Amplitude f. (genitive Amplitude, plural Amplituden)

1. amplitude (mathematics, physics)

# Strategy wiki

Up to date as of January 23, 2010

### From StrategyWiki, the free strategy guide and walkthrough wiki

Amplitude
Developer(s) Harmonix
Publisher(s) Sony Computer Entertainment
Release date(s)
Genre(s) Music
System(s) PlayStation 2
Players Single player, Multiplayer
Rating(s)
ESRB: Teen
PEGI: Ages 12+
Preceded by Frequency

Amplitude is a music rhythm game for the PlayStation 2. The game is the sequel to Frequency, and retains most of the gameplay with some graphical changes and different music. Gutiar Hero and Rock Band, also developed by Harmonix, retain many elements from this game and its predecessor.

The majority of the music is licensed from popular bands in various genres of music, though some is contributed from one of the members of the development team and his band.

Online play is no longer available in the U.S. due to Sony shutting down the servers for the game in early 2007. Multiplayer is still available for 2–4 players on the same PS2.

In Amplitude, the player controls a ship (referred to as a "Beat Blaster") moving down a path of varying shapes and lengths, containing up to six tracks. Each color-coded track corresponds to a different aspect of the song, such as percussion, synth, bass, or vocals, and contains a sequence of notes. As the player hits buttons corresponding to the note placement on the track, the notes activate a small portion of the track. If the player successfully activates enough notes in sequence, the track is "captured" and the section will play automatically for a number of bars, freeing the player to capture another section.

The object of the game is to capture a sufficient amount of sections to reach the end of the song. If the player continually misses notes, an energy meter empties until the game is over.

Appendices

# Simple English

[[File:|thumb|thumb|350px|In this picture, y is the amplitude of the wave]]

File:Sinus amplitude
Different kinds of amplitudes

The amplitude or peak amplitude of a wave is a measure of how big its oscillation is. Amplitudes are always positive numbers (for example: 3.5, 1, 120) and are never negative (for example: -3.5, -1, -120). Amplitudes are positive because distance can only be greater than zero or equal to zero; negative distance does not exist.

The distance from the top of one peak to the bottom of another is called peak-to-peak amplitude. Another way to describe peak-to-peak amplitude is to say that it is the distance between the maximum positive value and the maximum negative value of a wave.

## Other pages

Simple English Wiktionary has the word meaning for: