Amplitude

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Amplitude

Amplitude is the magnitude

Magnitude (mathematics)

The magnitude of a mathematical object is its size: a property by which it can be larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs....
of change in the oscillating variable, with each oscillation

Oscillation

Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and Alternating current power....
, within an oscillating system. For instance, sound waves are oscillations in atmospheric pressure

Atmospheric pressure

Atmospheric pressure is sometimes defined as the force per unit area exerted against a surface by the weight of air above that surface at any given point in the Earth's atmosphere....
and their amplitudes are proportional to the change in pressure

Pressure

Pressure is the force per unit area applied to an object in a direction surface normal to the surface. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure....
during one oscillation. If the 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

Extrema

Extrema may refer to:In Mathematics:*maxima and minimaIn Music:*Extrema , an Italian metal band...
of the curve.

In older texts the phase

Phase (waves)

The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0....
is sometimes very confusingly called the amplitude.

-to-peak amplitude is the measure of the change between peak and trough.

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Encyclopedia

Amplitude is the magnitude

Magnitude (mathematics)

Oscillation

Atmospheric pressure

Pressure

Extrema

Extrema may refer to:In Mathematics:*maxima and minimaIn Music:*Extrema , an Italian metal band...
of the curve.

In older texts the phase

Phase (waves)

Concepts of amplitude

Peak-to-peak amplitude

Peak-to-peak amplitude is the measure of the change between peak and trough. Peak-to-peak amplitudes can be measured by meter

Measuring instrument

In the physical sciences, quality assurance, and engineering, measurement is the activity of obtaining and comparing physical quantity of real-world object and phenomenon....
s with appropriate circuitry, or by viewing the waveform on an oscilloscope

Oscilloscope

An oscilloscope is a type of electronic test instrument that allows signal voltages to be viewed, usually as a two-dimensional graph of one or more electrical potential differences plotted as a function of time or of some other voltage ....
. Peak-to-peak is a straightforward measurement to make on an oscilloscope, the peaks of the waveform being easily identified and measured against the graticule

Oscilloscope

An oscilloscope is a type of electronic test instrument that allows signal voltages to be viewed, usually as a two-dimensional graph of one or more electrical potential differences plotted as a function of time or of some other voltage ....
. It remains a common way of specifying amplitude but sometimes other measures of amplitude are more appropriate.

Semi-amplitude

Semi-amplitude in fields such as astronomy

Astronomy

Astronomy is the science of Astronomical object and Phenomenon that originate outside the Earth's atmosphere . It is concerned with the evolution, physics, chemistry, meteorology, and motion of celestial objects, as well as the physical cosmology....
is understood to mean half the peak-to-peak amplitude.

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

Root mean square amplitude

Root mean square
Root mean square

In mathematics, the root mean square , also known as the quadratic mean, is a statistics measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids....
(RMS) amplitude is used especially in electrical engineering

Electrical engineering

Electrical engineering, sometimes referred to as electrical and electronic engineering, is a field of engineering that deals with the study and application of electricity, electronics and electromagnetism....
: the RMS is defined as the square root

Square root

In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x....
of the mean

Mean

In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....
over time of the square of the vertical distance of the graph from the rest state.

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

Power (physics)

In physics, power is the rate at which mechanical work is performed or energy is transmitted, or the amount of energy required or expended for a given unit of time....
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

Alternating current

In alternating current the movement of electric charge periodically reverses direction. An electric charge would for instance move forward, then backward, then forward, then backward, over and over again....
electrical power

Electric power

Electric power is defined as the rate at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt .When electric current flows in a circuit, it can transfer energy to do mechanical work or work ....
it is universal to specify RMS values of a sinusoidal waveform. The peak-to-peak voltage of a sine wave is nearly 3 times the RMS value, but is a rarely used measure in this field. Some common meter types

Voltmeter

A voltmeter is an instrument used for measuring the electrical potential difference between two points in an electric circuit. Analog voltmeters move a pointer across a scale in proportion to the voltage of the circuit; digital voltmeters give a numerical display of voltage by use of an analog to digital converter....
used in electrical engineering are calibrated for RMS amplitude, but actually operate on a DC input. Digital voltmeters and moving coil meters are both in this category. Such meters require the AC input to be first rectified

Rectifier

A rectifier is an electrical device that converts alternating current to direct current , a process known as rectification. Rectifiers have many uses including as components of power supply and as detector s of radio signals....
and are really reading proportional to either rectified average or peak amplitiude. They are not true RMS meters and the RMS calibration is only correct for a sine wave input since the ratio between peak, average and rms values is dependant on waveform

Waveform

Waveform means the shape and form of a signal such as a wave moving in a solid, liquid or gaseous medium.In many cases the medium in which the wave is being propagated does not permit a direct visual image of the form....
. True RMS meters do exist but are more specialised equipment.

Ambiguity of amplitude

The use of peak amplitude is simple and unambiguous for symmetric, periodic waves, like a sine

Siné

Maurice Sinet, known as Sin? is a France cartoonist.As a young man he studied drawing and graphic arts, earning his life as a cabaret singer....
wave, a square wave

Square wave

A square wave is a kind of non-sinusoidal waveform, most typically encountered in electronics and signal processing. An ideal square wave alternates regularly and instantaneously between two levels....
, 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. In electrical engineering the usual solution to this ambiguity is to measure the amplitude from a defined reference potential (such as ground

Ground (electricity)

In electrical engineering, ground or earth may be the reference point in an electrical circuit from which other voltages are measured, or a common return path for electric current, or a direct physical connection to the Earth....
or 0V). Strictly speaking, this is no longer amplitude since there is the possibly that a constant (DC component) is included in the measurement.

Pulse amplitude

In telecommunication

Telecommunication

Telecommunication is the assisted Transmission of Signal over a distance for the purpose of communication. In earlier times, this may have involved the use of smoke signals, Drum , Semaphore line, flag signals or heliograph....
, pulse amplitude is the magnitude of a pulse

Pulse (signal processing)

In signal processing, the term pulse has the following meanings:#A rapid, transient change in the amplitude of a Signalling from a baseline value to a higher or lower value, followed by a rapid return to the baseline value....
parameter, such as the field intensity, voltage

Voltage

Electrical tension is the potential difference between two points of an electrical or electronic circuit, expressed in volts. It is the measurement of the potential for an electric field to cause an electric current in an electrical conductor....
level, current

Electric current

Electric current is the flow of electric charge. The electric charge may be either electrons or ions.The International System of Units unit of electric current intensity is the ampere....
level, or power

Power (physics)

In physics, power is the rate at which mechanical work is performed or energy is transmitted, or the amount of energy required or expended for a given unit of time....
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

Root mean square

In mathematics, the root mean square , also known as the quadratic mean, is a statistics measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids....
."

Note 2: Pulse amplitude also applies to the amplitude of frequency

Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
- and phase

Phase (waves)

The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0....
-modulated waveform

Waveform

Federal Standard 1037C

Federal Standard 1037C, entitled Telecommunications: Glossary of Telecommunication Terms is a United States Federal Standard, issued by the General Services Administration pursuant to the Federal Property and Administrative Services Act of 1949, as amended....

Amplitude in the wave equation

In the simple wave equation

Wave equation

The wave equation is an important second-order linear partial differential equation that describes the propagation of a variety of waves, such as sound waves, light waves and water waves....

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

Vibrating string

A vibration in a strings is a wave. Usually a vibrating string produces a sound whose frequency in most cases is constant. Therefore, since frequency characterizes the Pitch_, the sound produced is a constant note....
, or in medium such as water

Water

Water is a common chemical substance that is essential for the survival of all known forms of life. In typical usage, water refers only to its liquid form or States of matter, but the substance also has a solid state, ice, and a gaseous state, water vapor or steam....
, the amplitude is a displacement

Displacement (vector)

In physics, displacement is the vector that specifies the change in position of a point or a particle in reference to a previous position. When the previous point is the origin, this is better referred to as a position vector....
.

The amplitude of sound waves and audio signals (which relates to the volume) conventionally refers to the amplitude of the air pressure

Sound

Sound is vibration transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a threshold of hearing to be heard, or the sensation stimulated in organs of hearing by such vibrations....
in the wave, but sometimes the amplitude of the displacement

Particle displacement

Particle displacement or particle amplitude is a measurement of distance of the movement of a particle in a medium as it transmits a wave....
(movements of the air or the diaphragm of a speaker

Loudspeaker

A loudspeaker, speaker, or speaker system is an electroacoustical transducer that converts an electricity signal processing to sound....
) is described. The logarithm

Logarithm

In mathematics, the logarithm of a number to a given base is the Power or exponent to which the base must be raised in order to produce the number....
of the amplitude squared is usually quoted in dB

Decibel

The decibel is a logarithmic units of measurement that expresses the magnitude of a physical quantity relative to a specified or implied reference level....
, so a null amplitude corresponds to -8

Infinity

Infinity comes from the Latin infinitas or "unboundedness." It refers to several distinct concepts – usually linked to the idea of "without end" – which arise in philosophy, mathematics, and theology....
dB. Loudness

Loudness

Loudness is the quality of a sound that is the primary psychological correlate of physical strength .Loudness, a subjective measure, is often confused with objective measures of sound pressure such as decibels or sound intensity....
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

Sound intensity

The sound intensity, I, is defined as the sound power Pac per unit area A. The usual context is the noise measurement of sound intensity in the air at a listener's location....
of the wave.

For electromagnetic radiation

Electromagnetic radiation

Electromagnetic radiation takes the form of wave propagation waves in a vacuum or in matter. EM radiation has an electric field and magnetic field component which oscillate in phase perpendicular to each other and to the direction of energy Wave propagation....
, the amplitude of a photon corresponds to the changes in the electric field

Electric field

In physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field ....
of the wave. However radio signals may be carried by electromagnetic radiation; the intensity of the radiation (amplitude modulation

Amplitude modulation

Amplitude modulation is a technique used in electronic communication, most commonly for transmitting information via a radio carrier wave....
) or the frequency of the radiation (frequency modulation

Frequency modulation

In telecommunications, frequency modulation conveys information over a carrier wave by varying its frequency . In analog signal applications, the instantaneous frequency of the carrier is directly proportional to the instantaneous value of the input signal....
) is oscillated and then the individual oscillations are varied (modulated) to produce the signal.

Waveforms and amplitude

The amplitude may be constant (in which case the wave is a continuous wave

Continuous wave

A continuous wave or continuous waveform is an electromagnetic wave of constant amplitude and frequency; and in mathematical analysis, of infinite duration....
) or may vary with time and/or position. The form of the variation of amplitude is called the envelope

Envelope detector

An envelope detector is an electronic circuit that takes a high-frequency signal as input, and provides an output which is the "envelope" of the original signal....
of the wave.

If the waveform is a pure sine wave

Sine wave

The sine wave or sinusoid is a function that occurs often in mathematics, physics, signal processing, hearing , electrical engineering, and many other fields....
, the relationships between peak-to-peak, peak, mean, and RMS

Root mean square

In mathematics, the root mean square , also known as the quadratic mean, is a statistics measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids....
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

Sine wave

The sine wave or sinusoid is a function that occurs often in mathematics, physics, signal processing, hearing , electrical engineering, and many other fields....
the relationship between RMS and peak-to-peak amplitude is:

Amplitude

Concepts of amplitude

Peak-to-peak amplitude

Semi-amplitude

Root mean square amplitude

Ambiguity of amplitude

Pulse amplitude

Amplitude in the wave equation

Units of amplitude

Waveforms and amplitude

See also

Further reading