Amplitude

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

the distance y 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:

1. 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
2. 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.
3. 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 waves on a string, the amplitude is a distance.

For sound waves and audio signals, the amplitude corresponds to the air pressure, or to the movements of the diaphragm of a speaker. Its logarithm is usually measured in dB, so a null amplitude corresponds to -inf dB.

For electromagnetic waves, the amplitude corresponds to the electric field.

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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Compare

• frequency
• period
• wavelength

See also

• wave
• amplitude modulation