Amplitude

Amplitude is a nonnegative scalar measure of a wave's magnitude of oscillation. In the following diagram,

the distance x is the amplitude of the wave. Sometimes that distance is called the "peak amplitude", distinguishing it from another concept of amplitude, used especially in electrical engineering: the root mean square amplitude, defined as the square root of the mean of the square of the maximum vertical distance of this graph from the horizontal axis.

There are a few ways to formalize amplitude:

The amplitude of a wave is the absolute value of the magnitude of the disturbance of the point/particule most disturbed by the wave in one cycle
Amplitude is the absolute value of the magnitude of the displacement of a wave from a mean value. Typically the mean value is taken as half of displacement_max-displacement_min.
Amplitude is the absolute value of one-half of the mean distance (or difference) between maxima and minima.

The third definition is often used for "complex" waveforms. (Why?)

to do: compare when/how these are equivalent or not, and when to use them

In the simple wave equation

y = A sin(t − k) + b

A is the amplitude of the wave.

The amplitude of a wave is the measure of the magnitude of the maximum disturbance in the medium during one wave cycle, and is measured in units depending on the type of wave. For examples, waves on a string have an amplitude expressed as a distance (meters), sound waves as pressure (pascals) and electromagnetic waves as the amplitude of the electric field (volts/meter). The amplitude may be constant (in which case the wave is a c.w. or continuous wave) or may vary with time and/or position. The form of the variation of amplitude is called the envelope of the wave.

Compare: frequency, period, wavelength

See: wave\n