amplitude

In a wave or oscillation, the maximum displacement from equilibrium or rest position; symbol A. It is always a positive number.

For quantum-mechanical amplitude, see probability amplitude. For the video game of the same name, see Amplitude (game).

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

In the following diagram,

the displacement y is the amplitude of the wave.

Sometimes this distance is called the "peak amplitude", distinguishing it from another concept of amplitude, used especially in electrical engineering: the root mean square (RMS) 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 unsymmetric wave, for example periodic pulses in one direction, 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 and then divided by two. 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

A is the amplitude of the wave.

The amplitude of sound waves and audio signals 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.