Definition

Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation. If a 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 and the equilibrium value.

Peak-to-peak amplitude is the change between peak (highest amplitude value) and trough (lowest amplitude value, which can be negative). With appropriate circuitry, peak-to-peak amplitudes can be measured by meters or by viewing the waveform on an oscilloscope. Peak-to-peak is a straightforward measurement on an oscilloscope, the peaks of the waveform being easily identified and measured against the graticule. This remains a common way of specifying amplitude, but sometimes other measures of amplitude are more appropriate.

In audio system measurements, telecommunications and other areas where the measured is a signal that swings above and below a zero value but is not sinusoidal, peak amplitude is often used. This is the maximum absolute value of the signal.

Semi-amplitude means half the peak-to-peak amplitude. It is the most widely used measure of orbital amplitude in astronomy and the measurement of small semi-amplitudes of nearby stars is important in the search for exoplanets. For a sine wave, peak amplitude and semi-amplitude are the same.

Some scientists use “amplitude” or “peak amplitude” to mean semi-amplitude, that is, half the peak-to-peak amplitude.

In this simple wave equation

$$ x = A\sin \left( {t - K} \right) + b $$

where 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 a 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 \( - \infty \) dB. Loudness is related to amplitude and intensity and is one of the 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.