Amplitude is the magnitude of change in the oscillating variable, with each oscillation, within an oscillating system. For instance, sound waves are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation. If a graph of the system is drawn with the oscillating variable as the vertical axis and time as the horizontal axis then the amplitude may be measured as the vertical distance between points on the curve.
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).
When dealing with alternating current electrical power it is universal to specify RMS values of a sinusoidal waveform. It is important to recognize that the peak-to-peak voltage is nearly 3 times the RMS value when assessing safety, specifying components, etc.
Note 1: Pulse amplitude is measured with respect to a specified reference and therefore should be modified by qualifiers, such as "average", "instantaneous", "peak", or "root-mean-square."
Source: from Federal Standard 1037C
In the simple wave equation
A is the amplitude of the wave.
The units of the amplitude depend on the type of wave.
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. 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.
If the waveform is a pure sine wave, the relationships between peak-to-peak, peak, mean, and RMS amplitudes are fixed and known, but this is not true for an arbitrary waveform which may or may not be periodic.
For a sine wave the relationship between RMS and peak-to-peak amplitude is: