# Amplitude

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.

## Concepts of Amplitude

### Peak Amplitude

Peak amplitude is measured between a peak and the rest position of the system. In many sciences this is called peak amplitude. In astronomy, when measuring the wobble of a body due to the gravitational influence of another body, it is called the semi-amplitude.

File:Wave.png
The displacement y is the amplitude of the wave

### Peak-to-peak Amplitude

Peak-to-peak amplitude is to measure it between peak and trough. Peak-to-peak amplitudes can be measured by meters with appropriate circuitry, or by viewing the waveform on an oscilloscope.

### Root Mean Square Amplitude

Root mean square(RMS) amplitude is used especially in electrical engineering: the RMS is defined as the square root of the mean over time of the square of the vertical distance of the graph from the rest state.

### Ambiguity of Amplitude

The use of peak amplitude is simple and unambiguous for symmetric, periodic waves, like a sine wave, a square wave, or a triangular wave. For an asymmetric wave (periodic pulses in one direction, for example), 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 (the peak-to-peak amplitude) and then divided by two.

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).

File:Sine voltage.svg
A sinodial voltage.
1 = Amplitude (peak),
2 = Peak-to-peak,
3 = RMS,
4 = Wave period

When dealing with alternating current electrical power it is universal to specify RMS values of a sinusoidal waveform. It is important to recognise that the peak-to-peak voltage is nearly 3 times the RMS value when assessing safety, specifying components, etc.

### Pulse amplitude

In telecommunication, pulse amplitude is the magnitude of a pulse parameter, such as the field intensity, voltage level, current level, or power level.

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."

Note 2: Pulse amplitude also applies to the amplitude of frequency- and phase-modulated waveform envelopes.

Source: from Federal Standard 1037C

## Amplitude in the Wave Equation

In the simple wave equation

$x=A\sin(t-K)+b\ ,$ A is the amplitude of the wave.

## Units of Amplitude

The units of the amplitude depend on the type of wave.

For waves on a string, or in medium such as water, the amplitude is a displacement.

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.

## Wave Forms and Amplitude

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.

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:

${\mbox{Peak-to-peak}}=2{\sqrt {2}}\times {\mbox{RMS}}\approx 2.8\times {\mbox{RMS}}.\,$  