Amplitude

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For quantum-mechanical amplitude, see probability amplitude. For the video game of the same name, see Amplitude (video game).

The amplitude is a nonnegative scalar measure of a wave's magnitude of oscillation, that is, the magnitude of the maximum disturbance in the medium during one wave cycle.

Image:Wave.png

The displacement y is the amplitude of the wave

Sometimes this distance is called the peak amplitude, distinguishing it from another concept of amplitude, used especially in electrical engineering: the RMS or root mean square amplitude, defined as the square root of the temporal mean of the square of the vertical distance of this graph from the horizontal axis. The use of peak amplitude is 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).

Image:Sine voltage.svg

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

1 Formalize amplitude
2 Pulse amplitude
3 Peak-to-peak
4 See also

[edit] Formalize amplitude

There are a few ways to formalize amplitude:

In the simple wave equation

Failed to parse (Missing texvc executable; please see math/README to configure.): x = A \sin(t - K) + b\ ,

A is the amplitude of the wave.

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.

For electromagnetic radiation, the amplitude corresponds to the electric field of the wave. The square of the amplitude is proportional to the intensity of the wave.

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.

[edit] 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

[edit] Peak-to-peak

Image:Sine voltage.svg

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

The peak-to-peak amplitude of a waveform is the amplitude between its maximum positive value and its maximum negative value. The peak value is the maximum amplitude above zero.

Typically used in electrical engineering and electronics to characterise a varying voltage or current.

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.

Peak-to-peak amplitudes can be measured by meters with appropriate circuitry, or by viewing the waveform on an oscilloscope.

For a sine wave the relationship between RMS and peak-to-peak amplitude is:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mbox{Peak-to-peak} = 2 \sqrt{2} \times \mbox{RMS} \approx 2.8 \times \mbox{RMS}. \,

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.

Peak-to-peak voltage (pk-pk, or V_p-p), is the voltage from the lowest (minimum) to the highest (maximum) voltage of an electronics signal.