# Amplitude

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The amplitude is a nonnegative scalar measure of a wave's magnitude of oscillation, that is, the magnitude of the maximum disturbance in the medium during one wave cycle.

Sometimes this distance is called the peak amplitude, distinguishing it from another concept of amplitude, used especially in electrical engineering: the RMS or root mean square amplitude, defined as the square root of the temporal mean of the square of the vertical distance of this graph from the horizontal axis. The use of peak amplitude is 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 the maximum negative signal (the peak-to-peak amplitude) and then divided by two.

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).

There are a few ways to formalize amplitude:

In the simple wave equation

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

A is the amplitude of the wave.

The units of the amplitude depend on the type of wave.

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

The amplitude of sound waves and audio signals (also referred to as 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.

For electromagnetic radiation, the amplitude corresponds to the electric field of the wave. The square of the amplitude is proportional to the intensity of the wave.

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.

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