Amplitude is the magnitude The magnitude of a mathematical object is its size: a property by which it can be compared as 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 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 AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes is used to be synonymous with "oscillation.& within an oscillating system. For example, sound waves Sound is a travelling wave which is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations in air are oscillations in atmospheric pressure Atmospheric pressure is the force per unit area exerted against a surface by the weight of air above that surface in the Earth's atmosphere. In most circumstances atmospheric pressure is closely approximated by the hydrostatic pressure caused by the weight of air above the measurement point. Low pressure areas have less atmospheric mass above and their amplitudes are proportional to the change in pressure Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient 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.

In older texts the phase 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. Phase is a frequency domain or Fourier transform domain concept, and as such, can be readily understood in terms of simple harmonic motion. The same concept applies to wave motion, is sometimes very confusingly called the amplitude.^[1]

Concepts

Peak-to-peak amplitude

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 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 (vertical(Y) axis) plotted as a function of time or of some other voltage (horizontal(x) axis). Although an oscilloscope displays voltage on its vertical axis, any. Peak-to-peak is a straightforward measurement on an oscilloscope, the peaks of the waveform being easily identified and measured against the graticule 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 (vertical(Y) axis) plotted as a function of time or of some other voltage (horizontal(x) axis). Although an oscilloscope displays voltage on its vertical axis, any. This remains a common way of specifying amplitude, but sometimes other measures of amplitude are more appropriate.

Peak amplitude

In audio system measurements Audio system measurements are made for several purposes. Designers take measurements so that they can specify the performance of a piece of equipment. Maintenance engineers make them to ensure equipment is still working to specification, or to ensure that the cumulative defects of an audio path are within limits considered acceptable. Some aspects, telecommunications Telecommunication is the transmission of messages, over significant distances, for the purpose of communication. In earlier times, telecommunications involved the use of visual signals, such as smoke, semaphore telegraphs, signal flags, and optical heliographs, or audio messages via coded drumbeats, lung-blown horns, or sent by loud whistles, for and other areas where the measurand is a signal that swings above and below a zero value but is not sinusoidal The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. It occurs often in pure mathematics, as well as physics, signal processing, electrical engineering and many other fields. Its most basic form as a function of time is:, peak amplitude is often used. This is the absolute value In mathematics, the absolute value |a| of a real number a is a's numerical value without regard to its sign. So, for example, 3 is the absolute value of both 3 and −3 of the signal.

Semi-amplitude

Semi-amplitude means half the peak-to-peak amplitude^[2]. It is the most widely used measure of orbital amplitude in astronomy Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the Earth's atmosphere (such as the cosmic background radiation). It is concerned with the evolution, physics, chemistry, meteorology, and motion of celestial objects, as well as the formation and development of the universe and the measurement of small semi-amplitudes of nearby stars is important in the search for exoplanets An extrasolar planet, or exoplanet, is a planet outside the Solar System. As of 27 April 2010)[update], astronomers have made confirmed detections of 453 such planets. The vast majority have been observed through radial velocity observations and other indirect methods rather than actual imaging. Most are giant planets thought to resemble Jupiter;.^[3] For a sine wave, peak amplitude and semi-amplitude are the same.

Some scientists^[4] use "amplitude" or "peak amplitude" to mean semi-amplitude, that is, half the peak-to-peak amplitude.^[2]

Root mean square amplitude

Root mean square In mathematics, the root mean square , also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids. RMS is used in various fields, including electrical engineering; one of the more prominent uses of RMS is in the field of signal (RMS) amplitude is used especially in electrical engineering Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical power supply. It now covers a range of subtopics: the RMS is defined as the 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 There are other statistical measures that use samples that some people confuse with averages - including 'median' and 'mode'. Other simple statistical analyses use measures of spread, such as range, interquartile range, or standard deviation. For a real-valued random variable X, the mean is the expectation of X. Note that not every probability over time of the square of the vertical distance of the graph from the rest state.^[5]

For complex waveforms, especially non-repeating signals like noise, the RMS amplitude is usually used because it is both unambiguous and has physical significance. For example, the average power The dimension of power is energy divided by time. The SI unit of power is the watt , which is equal to one joule per second. Non-SI units of power include ergs per second (erg/s), horsepower (hp), metric horsepower (Pferdestärke (PS) or cheval vapeur, CV), and foot-pounds per minute. One horsepower is equivalent to 33,000 foot-pounds per minute, transmitted by an acoustic or electromagnetic wave Electromagnetic radiation is a phenomenon that takes the form of self-propagating waves in a vacuum or in matter. It consists of electric and magnetic field components which oscillate in phase perpendicular to each other and perpendicular to the direction of energy propagation. Electromagnetic radiation is classified into several types according 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).^[6]

For alternating current In alternating current the movement (or flow) of electric charge periodically reverses direction. An electric charge would for instance move forward, then backward, then forward, then backward, over and over again. In direct current (DC), the movement (or flow) of electric charge is only in one direction electrical 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, the universal practice is 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 rarely used. Some common meter types 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. Both digital voltmeters and moving coil meters are in this category. Such meters require the AC input to be first rectified A rectifier is an electrical device that converts alternating current to direct current (DC), a process known as rectification. Rectifiers have many uses including as components of power supplies and as detectors of radio signals. Rectifiers may be made of solid state diodes, vacuum tube diodes, mercury arc valves, and other components. They are not true RMS meters, but rather, are reading proportional to either rectified average or peak amplitude. 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 means the shape and form of a signal such as a wave moving in a solid, liquid or gaseous medium or a vacuum. Until recently, true RMS meters were mostly used only in radio frequency Radio frequency is a rate of oscillation in the range of about 30 kHz to 300 GHz, which corresponds to the frequency of electrical signals normally used to produce and detect radio waves. RF usually refers to electrical rather than mechanical oscillations, although mechanical RF systems do exist (see mechanical filter and RF MEMS) measurements. These instruments based their measurement on detecting the heating effect in a load resistor with a thermistor A thermistor is a type of resistor whose resistance varies with temperature. The word is a portmanteau of thermal and resistor. Thermistors are widely used as inrush current limiters, temperature sensors, self-resetting overcurrent protectors, and self-regulating heating elements. The advent of microprocessor A microprocessor incorporates most or all of the functions of a computer's central processing unit on a single integrated circuit (IC, or microchip). The first microprocessors emerged in the early 1970s and were used for electronic calculators, using binary-coded decimal (BCD) arithmetic in 4-bit words. Other embedded uses of 4-bit and 8-bit controlled meters capable of calculating RMS by sampling In signal processing, sampling is the reduction of a continuous signal to a discrete signal. A common example is the conversion of a sound wave to a sequence of samples (a discrete-time signal) the waveform has made true RMS measurement commonplace.

Ambiguity

In general, the use of peak amplitude is simple and unambiguous only for symmetric periodic waves, like a sine In mathematics, the trigonometric functions are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications wave, a 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. This is because the value 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 to 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 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 possibility that a constant (DC component) is included in the measurement.

Pulse amplitude

In telecommunication Telecommunication is the transmission of messages, over significant distances, for the purpose of communication. In earlier times, telecommunications involved the use of visual signals, such as smoke, semaphore telegraphs, signal flags, and optical heliographs, or audio messages via coded drumbeats, lung-blown horns, or sent by loud whistles, for, pulse amplitude is the magnitude of a pulse These can be found in pulse waves, square waves, boxcar functions, and rectangular functions. In digital signals the up and down transitions between high and low levels are called the rising edge and the falling edge. In digital systems the detection of these sides or action taken in response is termed edge-triggered, rising or falling depending parameter, such as the voltage The voltage between two points is a short name for the electrical force that would drive an electric current between those points. Specifically, voltage is equal to energy per unit charge. In the case of static electric fields, the voltage between two points is equal to the electrical potential difference between those points. In the more general level, current Electric current means, depending on the context, a flow of electric charge or the rate of flow of electric charge (a quantity). This flowing electric charge is typically carried by moving electrons, in a conductor such as wire; in an electrolyte, it is instead carried by ions, and, in a plasma, by both level, field intensity, or power The dimension of power is energy divided by time. The SI unit of power is the watt , which is equal to one joule per second. Non-SI units of power include ergs per second (erg/s), horsepower (hp), metric horsepower (Pferdestärke (PS) or cheval vapeur, CV), and foot-pounds per minute. One horsepower is equivalent to 33,000 foot-pounds per minute, level.

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 In mathematics, the root mean square , also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids. RMS is used in various fields, including electrical engineering; one of the more prominent uses of RMS is in the field of signal".

Pulse amplitude also applies to the amplitude of 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. Loosely speaking, 1 year is the period of the Earth's orbit around the Sun, and the Earth's rotation on its axis has- and phase 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. Phase is a frequency domain or Fourier transform domain concept, and as such, can be readily understood in terms of simple harmonic motion. The same concept applies to wave motion,-modulated waveform Waveform means the shape and form of a signal such as a wave moving in a solid, liquid or gaseous medium or a vacuum envelopes.^[7]

Formal representation

In this simple wave equation The wave equation is an important second-order linear partial differential equation of waves, such as sound waves, light waves and water waves. It arises in fields such as acoustics, electromagnetics, and fluid dynamics. Historically, the problem of a vibrating string such as that of a musical instrument was studied by Jean le Rond d'Alembert,

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 A vibration in a string 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. Vibrating strings are the basis of any string instrument like guitar, cello, or piano, or in medium such as water Water is a chemical substance with the chemical formula H2O. Its molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state, water vapor or steam, the amplitude is a displacement A displacement is the shortest distance from the initial and final positions of a point P. Thus, it is the length of an imaginary straight path, typically distinct from the path actually travelled by P. A displacement vector represents the length and direction of that imaginary straight path.

The amplitude of sound waves and audio signals (which relates to the volume) conventionally refers to the amplitude of the air pressure Sound is a travelling wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong 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 or particle amplitude is a measurement of distance (in metres) of the movement of a particle in a medium as it transmits a wave. In most cases this is a longitudinal wave of pressure (such as sound), but it can also be a transverse wave, such as the vibration of a taut string. In the case of a sound wave travelling through (movements of the air or the diaphragm of a speaker A loudspeaker is an electroacoustic transducer that converts an electrical signal into sound. The speaker moves in accordance with the variations of an electrical signal and causes sound waves to propagate through a medium such as air or water) 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.

Waveform and envelope

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, as they are for any continuous periodic wave. However, this is not true for an arbitrary waveform which may or may not be periodic or continuous.

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

.

For other waveforms the relationships are not (necessarily) arithmetically the same as they are for sine waves.

See also

• Waves and their properties:
  • Frequency
  • Period
  • Wavelength
  • Crest factor
• Amplitude modulation

Notes

1. ^ Knopp, Konrad; Bagemihl, Frederick (1996). Theory of Functions Parts I and II. Dover Publications. p. 3. ISBN 0-486-69219-1.
2. ^ ^{a b} Tatum, J. B. Physics - Celestial Mechanics. Paragraph 18.2.12. 2007. Retrieved 2008-08-22.
3. ^ Uriel A. Goldvais. Exoplanets, pp.2-3.
4. ^ Regents of the University of California. Universe of Light: What is the Amplitude of a Wave? 1996. Retrieved 2008-08-22
5. ^ Department of Communicative Disorders University of Wisconsin–Madison. RMS Amplitude. Retrieved 2008-08-22
6. ^ Ward, Electrical Engineering Science, pp141-142, McGraw-Hill, 1971.
7. ^ This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C".

Categories: Physical quantities | Sound | Fundamental physics concepts

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