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any disturbance that travels through an elastic medium such as air, ground, or water to be heard by the human ear. When a body vibrates, or moves back and forth (see vibrationvibration,
in physics, commonly an oscillatory motion—a movement first in one direction and then back again in the opposite direction. It is exhibited, for example, by a swinging pendulum, by the prongs of a tuning fork that has been struck, or by the string of a musical
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), the oscillation causes a periodic disturbance of the surrounding air or other medium that radiates outward in straight lines in the form of a pressure wavewave,
in physics, the transfer of energy by the regular vibration, or oscillatory motion, either of some material medium or by the variation in magnitude of the field vectors of an electromagnetic field (see electromagnetic radiation).
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. The effect these waves produce upon the ear is perceived as sound. From the point of view of physics, sound is considered to be the waves of vibratory motion themselves, whether or not they are heard by the human ear.

Generation of Sound Waves

Sound waves are generated by any vibrating body. For example, when a violin string vibrates upon being bowed or plucked, its movement in one direction pushes the molecules of the air before it, crowding them together in its path. When it moves back again past its original position and on to the other side, it leaves behind it a nearly empty space, i.e., a space with relatively few molecules in it. In the meantime, however, the molecules which were at first crowded together have transmitted some of their energy of motion to other molecules still farther on and are returning to fill again the space originally occupied and now left empty by the retreating violin string. In other words, the vibratory motion set up by the violin string causes alternately in a given space a crowding together of the molecules of air (a condensation) and a thinning out of the molecules (a rarefaction). Taken together a condensation and a rarefaction make up a sound wave; such a wave is called longitudinal, or compressional, because the vibratory motion is forward and backward along the direction that the wave is following. Because such a wave travels by disturbing the particles of a material medium, sound waves cannot travel through a vacuum.

Characteristics of Sound Waves

Sounds are generally audible to the human ear if their frequency (number of vibrations per second) lies between 20 and 20,000 vibrations per second, but the range varies considerably with the individual. Sound waves with frequencies less than those of audible waves are called subsonic; those with frequencies above the audible range are called ultrasonic (see ultrasonicsultrasonics,
study and application of the energy of sound waves vibrating at frequencies greater than 20,000 cycles per second, i.e., beyond the range of human hearing. The application of sound energy in the audible range is limited almost entirely to communications, since
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A sound wave is usually represented graphically by a wavy, horizontal line; the upper part of the wave (the crest) indicates a condensation and the lower part (the trough) indicates a rarefaction. This graph, however, is merely a representation and is not an actual picture of a wave. The length of a sound wave, or the wavelength, is measured as the distance from one point of greatest condensation to the next following it or from any point on one wave to the corresponding point on the next in a train of waves. The wavelength depends upon the velocity of sound in a given medium at a given temperature and upon the frequency of vibration. The wavelength of a sound can be determined by dividing the numerical value for the velocity of sound in the given medium at the given temperature by the frequency of vibration. For example, if the velocity of sound in air is 1,130 ft per second and the frequency of vibration is 256, then the wave length is approximately 4.4 ft.

The velocity of sound is not constant, however, for it varies in different media and in the same medium at different temperatures. For example, in air at 0°C;. it is approximately 1,089 ft per second, but at 20°C;. it is increased to about 1,130 ft per second, or an increase of about 2 ft per second for every centigrade degree rise in temperature. Sound travels more slowly in gases than in liquids, and more slowly in liquids than in solids. Since the ability to conduct sound is dependent on the density of the medium, solids are better conductors than liquids, liquids are better conductors than gases.

Sound waves can be reflected, refracted (or bent), and absorbed as light waves can be. The reflection of sound waves can result in an echoecho,
reflection of a sound wave back to its source in sufficient strength and with a sufficient time lag to be separately distinguished. If a sound wave returns within 1-10 sec, the human ear is incapable of distinguishing it from the orginal one.
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—an important factor in the acousticsacoustics
[Gr.,=the facts about hearing], the science of sound, including its production, propagation, and effects. Various branches of acoustics that deal with different aspects of sound and hearing include bioacoustics, physical acoustics, ultrasonics, and architectural
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 of theaters and auditoriums. A sound wave can be reinforced with waves from a body having the same frequency of vibration, but the combination of waves of different frequencies of vibration may produce "beats" or pulsations or may result in other forms of interferenceinterference,
in physics, the effect produced by the combination or superposition of two systems of waves, in which these waves reinforce, neutralize, or in other ways interfere with each other.
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Characteristics of Musical Sounds

Musical sounds are distinguished from noises in that they are composed of regular, uniform vibrations, while noises are irregular and disordered vibrations. Composers, however, frequently use noises as well as musical sounds. One musical tone is distinguished from another on the basis of pitch, intensity, or loudness, and quality, or timbre. Pitch describes how high or low a tone is and depends upon the rapidity with which a sounding body vibrates, i.e., upon the frequency of vibration. The higher the frequency of vibration, the higher the tone; the pitch of a siren gets higher and higher as the frequency of vibration increases. The apparent change in the pitch of a sound as a source approaches or moves away from an observer is described by the Doppler effectDoppler effect,
change in the wavelength (or frequency) of energy in the form of waves, e.g., sound or light, as a result of motion of either the source or the receiver of the waves; the effect is named for the Austrian scientist Christian Doppler, who demonstrated the effect
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. The intensity or loudness of a sound depends upon the extent to which the sounding body vibrates, i.e., the amplitude of vibration. A sound is louder as the amplitude of vibration is greater, and the intensity decreases as the distance from the source increases. Loudness is measured in units called decibelsdecibel
, abbr. dB, unit used to measure the loudness of sound. It is one tenth of a bel (named for A. G. Bell), but the larger unit is rarely used. The decibel is a measure of sound intensity as a function of power ratio, with the difference in decibels between two sounds being
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. The sound waves given off by different vibrating bodies differ in quality, or timbre. A note from a saxophone, for instance, differs from a note of the same pitch and intensity produced by a violin or a xylophone; similarly vibrating reeds, columns of air, and strings all differ. Quality is dependent on the number and relative intensity of overtones produced by the vibrating body (see harmonicharmonic.
1 Physical term describing the vibration in segments of a sound-producing body (see sound). A string vibrates simultaneously in its whole length and in segments of halves, thirds, fourths, etc.
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), and these in turn depend upon the nature of the vibrating body.


See G. Chedd, Sound (1970).


The mechanical excitation of an elastic medium. Originally, sound was considered to be only that which is heard. This admitted questions such as whether or not sound was generated by trees falling where no one could hear. A more mechanistic approach avoids these questions and also allows acoustic disturbances too high in frequency (ultrasonic) to be heard or too low (infrasonic) to be classed as extensions of those events that can be heard.

A source of sound undergoes rapid changes of shape, size, or position that disturb adjacent elements of the surrounding medium, causing them to move about their equilibrium positions. These disturbances in turn are transmitted elastically to neighboring elements. This chain of events propagates to larger and larger distances, constituting a wave traveling through the medium. If the wave contains the appropriate range of frequencies and impinges on the ear, it generates the nerve impulses that are perceived as hearing.

Acoustic pressure

A sound wave compresses and dilates the material elements it passes through, generating associated pressure fluctuations. An appropriate sensor (a microphone, for example) placed in the sound field will record a time-varying deviation from the equilibrium pressure found at that point within the fluid. The changing total pressure P measured will vary about the equilibrium pressure P0 by a small amount called the acoustic pressure, p = P - P0. The SI unit of pressure is the pascal (Pa), equal to 1 newton per square meter (N/m2). Standard atmospheric pressure (14.7 lb/in.2) is approximately 1 bar = 106 dyne/cm2 = 105 Pa. For a typical sound in air, the amplitude of the acoustic pressure may be about 0.1 Pa (one-millionth of an atmosphere); most sounds cause relatively slight perturbations of the total pressure. See Pressure, Pressure measurement, Pressure transducer, Sound pressure

Plane waves

One of the more basic sound waves is the traveling plane wave. This is a pressure wave progressing through the medium in one direction, say the +x direction, with infinite extent in the y and z directions. A two-dimensional analog is ocean surf advancing toward a very long, straight, and even beach. See Wave (physics), Wave equation, Wave motion

A most important plane wave, called harmonie, is the smoothly oscillating monofrequency plane wave described by Eq. (1).

The amplitude of this wave is P. The phase (argument of the cosine) increases with time, and at a point in space the cosine will pass through one full cycle for each increase in phase of 2&pgr;. The period T required for each cycle must therefore be such that 2&pgr;fT = 2&pgr;, or T = 1/f, so that f = 1/T can be identified as the frequency of oscillation of the pressure wave. During this period T, each portion of the waveform has advanced through a distance λ = cT, and this distance λ must be the wavelength. This gives the fundamental relation (2)
between the frequency, wavelength, and speed of sound c in any medium. For example, in air at room temperature the speed of sound is 343 m/s (1125 ft/s). A sound of frequency 1 kHz (1000 cycles per second) will have a wavelength of λ = c/f = 343/1000 m = m (1.1 ft). Lower frequencies will have longer wavelengths: a sound of 100 Hz in air has a wavelength of 3.4 m (11 ft). For comparison, in fresh water at room temperature the speed of sound is 1480 m/s (4856 ft/s), and the wavelength of 1-kHz sound is nearly 1.5 m (5 ft), almost five times greater than the wavelength for the same frequency in air.

Description of sound

The characterization of a sound is based primarily on human psychological responses to it. Because of the nature of human perceptions, the correlations between basically subjective evaluations such as loudness, pitch, and timbre and more physical qualities such as energy, frequency, and frequency spectrum are subtle and not necessarily universal.

The strength of a sound wave is described by its intensity. From basic physical principles, the instantaneous rate at which energy is transmitted by a sound wave through unit area is given by the product of acoustic pressure and the component of particle velocity perpendicular to the area. The time average of this quantity is the acoustic intensity. If all quantities are expressed in SI units (pressure amplitude or effective pressure amplitude in Pa, speed of sound in m/s, and density in kg/m3), then the intensity will be in watts per square meter (W/m2). See Sound intensity

Because of the way the strength of a sound is perceived, it has become conventional to specify the intensity of sound in terms of a logarithmic scale with the (dimensionless) unit of the decibel (dB). An individual with unimpaired hearing has a threshold of perception near 10-12 W/m2 between about 2 and 4 kHz, the frequency range of greatest sensitivity. As the intensity of a sound of fixed frequency is increased, the subjective evaluation of loudness also increases, but not proportionally. Rather, the listener tends to judge that every successive doubling of the acoustic intensity corresponds to the same increase in loudness. For sounds lying higher than 4 kHz or lower than 500 Hz, the sensitivity of the ear is appreciably lessened. Sounds at these frequency extremes must have higher threshold intensity levels before they can be perceived, and doubling of the loudness requires smaller changes in the intensity with the result that at higher levels sounds of equal intensities tend to have more similar loudnesses. It is because of this characteristic that reducing the volume of recorded music causes it to sound thin or tinny, lacking both highs and lows of frequency. Since most sound-measuring equipment detects acoustic pressure rather than intensity, it is convenient to define an equivalent scale in terms of the sound pressure level. The intensity level and sound-pressure level are usually taken as identical, but this is not always true. See Decibel

How “high” sound of a particular frequency appears to be is described by the sense of pitch. A few minutes with a frequency generator and a loudspeaker show that pitch is closely related to the frequency. Higher pitch corresponds to higher frequency, with small influences depending on loudness, duration, and the complexity of the waveform. For the pure tones (monofrequency sounds) encountered mainly in the laboratory, pitch and frequency are not found to be proportional. Doubling the frequency less than doubles the pitch. For the more complex waveforms usually encountered, however, the presence of harmonics favors a proportional relationship between pitch and frequency.

Propagation of sound

Plane waves are a considerable simplification of an actual sound field. The sound radiated from a source (such as a loudspeaker, a hand clap, or a voice) must spread outward much like the widening circles from a pebble thrown into a lake. A simple model of this more realistic case is a spherical source vibrating uniformly in all directions with a single frequency of motion. The sound field must be spherically symmetric with an amplitude that decreases with increasing distance from the source, and the fluid elements must have particle velocities that are directed radially.

Not all sources radiate their sound uniformly in all directions. When someone is speaking in an unconfined space, for example an open field, a listener circling the speaker hears the voice most well defined when the speaker is facing the listener. The voice loses definition when the speaker is facing away from the listener. Higher frequencies tend to be more pronounced in front of the speaker, whereas lower frequencies are perceived more or less uniformly around the speaker.


It is possible to hear but not see around the corner of a tall building. However, higher-frequency sound (with shorter wavelength) tends to bend or “spill” less around edges and corners than does sound of lower frequency. The ability of a wave to spread out after traveling through an opening and to bend around obstacles is termed diffraction. This is why it is often difficult to shield a listener from an undesired source of noise, like blocking aircraft or traffic noise from nearby residences. Simply erecting a brick or concrete wall between source and receiver is often an insufficient remedy, because the sounds may diffract around the top of the wall and reach the listeners with sufficient intensity to be distracting or bothersome. See Acoustic noise, Diffraction


Since the speed of sound varies with the local temperature (and pressure, in other than perfect gases), the speed of a sound wave can be a function of position. Different portions of a sound wave may travel with different speeds of sound.

Each small element of a surface of constant phase traces a line in space, defining a ray along which acoustic energy travels. The sound beam can then be viewed as a ray bundle, like a sheaf of wheat, with the rays distributed over the cross-sectional area of the surface of constant phase. As the major lobe spreads with distance, this area increases and the rays are less densely concentrated. The number of rays per unit area transverse to the propagation path measures the energy density of the sound at that point.

It is possible to use the concept of rays to study the propagation of a sound field. The ray paths define the trajectories over which acoustic energy is transported by the traveling wave, and the flux density of the rays measures the intensity to be found at each point in space. This approach, an alternative way to study the propagation of sound, is approximate in nature but has the advantage of being very easy to visualize.

Reflection and transmission

If a sound wave traveling in one fluid strikes a boundary between the first fluid and a second, then there may be reflection and transmission of sound. For most cases, it is sufficient to consider the waves to be planar. The first fluid contains the incident wave of intensity Ii and reflected wave of intensity Ir; the second fluid, from which the sound is reflected, contains the transmitted wave of intensity It. The directions of the incident, reflected, and transmitted plane sound waves may be specified by the grazing angles Θi, Θr, and Θt (measured between the respective directions of propagation and the plane of the reflecting surface). See Reflection of sound


When sound propagates through a medium, there are a number of mechanisms by which the acoustic energy is converted to heat and the sound wave weakened until it is entirely dissipated. This absorption of acoustic energy is characterized by a spatial absorption coefficient for traveling waves. See Sound absorption


The sensation stimulated in the auditory organs by a vibratory disturbance.



in the broad sense, the vibratory motion of the particles in anelastic medium, propagating as waves in gaseous, fluid, or solid mediums; in the narrow sense, a phenomenon that is perceived by a special sensory organ in humans and animals. Humans hear sound having a frequency between 16 and 20,000 hertz (Hz). The physical concept of sound includes both audible and inaudible sound. Sound with a frequency below 16 Hz is called infrasound; with a frequency above 20,000 Hz, ultrasound. Very high-frequency elastic waves in the range from 109 to 1012–1013 Hz are called hyper-sound. The infrasonic frequency region has virtually no lower limit; infrasonic vibrations are encountered in nature at frequencies of tenths and hundredths of a hertz. The frequency range of hypersonic waves is limited at the top by physical factors that characterize the atomic and molecular structure of the medium: the length of an elastic wave must be substantially greater than the free path length of molecules in gases and greater than the interatomic distances in fluids and solids. As a result, hypersound cannot propagate in air at a frequency of 109 Hz or higher or in solids at a frequency higher than 1012–1013” Hz.

Basic characteristics. An important characteristic of sound is its spectrum, which is produced by expanding the sound into simple harmonic vibrations (so-called frequency sound analysis). The spectrum is continuous if the energy of the sound vibrations is distributed continuously over a fairly broad frequency range; it is a linear spectrum if it has a set of discrete frequency components. Sound having a continuous spectrum is perceived as a noise like the rustling of leaves in the wind or the sounds of mechanisms in operation. A musical sound has a linear spectrum with multiple frequencies; the fundamental frequency determines the pitch of the sound as perceived by hearing, and the set of harmonic components distinguishes its timbre. The spectrum of speech sounds contains formants, which are stable groups of frequency components corresponding to certain phonetic elements. The energy parameter of sound vibrations is the sound intensity—the energy carried by the sound wave through a unit surface, perpendicular to the direction of propagation, per unit time. Sound intensity is a function of the sound pressure amplitude, as well as of the properties of the medium and the shape of the wave. The subjective parameter, which is associated with the intensity of the sound, is loudness, which is dependent on frequency. The human ear is most sensitive in the frequency range from 1 to 5 kHz. In this region the threshold of audibility—that is, the intensity of the weakest audible sounds—is on the order of 10-12 watts per sq m (W/m2), and the corresponding sound pressure is 10-5 new-tons per sq m (N/m2 ). The upper limit of intensity for sound perception by the human ear is called the threshold of pain; it is slightly dependent on frequency in the audible range and is approximately equal to 1 W/m2. Much greater intensities (up to 104 kW/m2) are achieved in ultrasonic technology.

Sound sources. Sound sources are phenomena that produce a local variation in pressure or mechanical stress. Vibrating solid bodies, such as the cones in loudspeakers, the diaphragms in telephones, and the strings and sounding boards in musical instruments, are the most common sound sources; in the ultrasonic frequency range the sources may be plates and rods made from piezoelectric or magnetostrictive materials. Vibrations of limited volumes of the medium itself—for example, in organ pipes, wind instruments, and whistles—may also be sound sources. The vocal apparatus of humans and animals is a complex vibratory system. The vibration of sound sources may be excited by a blow (in the case of a bell) or by plucking (in the case of a string); a self-excited vibration mode can be maintained in such objects by a current of air (in wind instruments). Electroacoustic transducers, in which mechanical vibrations are produced by converting electrical current oscillations of the same frequency, are a broad class of sound sources. In nature, sound is produced when air flows around solid bodies because of the creation and breakaway of vortices (for example, when the wind blows over wires, pipes, and the crests of ocean waves). Low-frequency and infrasonic sounds are produced by explosions and avalanches. The sources of acoustic noise include machines and mechanisms used in technology, as well as gas and water jets. The study of industrial, transportation, and aerodynamic sources of noise is receiving a great deal of attention in view of their harmful effects on the human body and industrial equipment.

Sound receivers. Sound receivers pick up sound energy and convert it into other forms. The hearing apparatus of humans and animals is in this category. In technology, electroacoustic transducers are generally used for the reception of sound: microphones in air, hydrophones in water, and geophones in the earth’s crust. In addition to such transducers, which reproduce the time dependence of the sound signal, there are receivers that measure the parameters of sound waves averaged with respect to time—for example, the Raleigh disk and the acoustic radiometer.

Propagation of sound waves. The propagation of sound waves is characterized primarily by the speed of sound. Longitudinal waves propagate in gaseous and fluid mediums (the direction of the particles’ vibratory motion coincides with the direction of propagation of the wave) at a velocity determined by the compressibility and density of the medium. The speed of sound in dry air at a temperature of 0°C is 330 m/sec, and in fresh water at 17°C it is 1,430 m/sec. In addition to longitudinal waves, transverse waves, for which the direction of the vibrations is perpendicular to the direction of propagation of the wave, as well as surface waves (Rayleigh waves), may propagate in solids. For most metals the velocity of longitudinal waves ranges from 4,000 to 7,000 m/sec; the velocity of transverse waves, between 2,000 and 3,500 m/sec.

During the propagation of waves of great amplitude, the compression phase propagates at a higher velocity than the rarefaction phase, so that the sinusoidal shape of the wave becomes gradually distorted and the sound wave is converted into a shock wave. In many cases sound dispersion is observed, that is, the velocity of propagation is a function of the frequency. Sound dispersion leads to a change in the shape of complex acoustic signals, including a number of harmonic components, and, in particular, to the distortion of sound pulses.

The phenomena of interference and diffraction, which are typical of all types of waves, can occur during the propagation of sound waves. When the size of obstacles and the inhomogeneities of the medium are large compared to the wavelength, the propagation of sound obeys the usual laws of reflection and refraction for waves and may be dealt with from the viewpoint of geometric acoustics.

During the propagation of a sound wave in a given direction, gradual attenuation occurs—that is, its intensity and amplitude decrease. Knowledge of the laws of attenuation is of practical importance in determining the maximum propagation distance for an acoustic signal. Attenuation depends on a number of factors, which become manifest to a greater or lesser degree according to the characteristics of the sound itself (primarily its frequency) and the properties of the medium. All of these factors may be classified in two large groups. The first group includes factors associated with the laws of wave propagation in the medium. Thus, in the case of propagation in an infinite medium, the intensity of a sound from a source of finite size decreases inversely as the square of the distance. Inhomogeneity of the medium’s properties causes scattering of the wave in various directions, thus weakening it in the original direction, as is the case with sound scattered by bubbles in water, by the agitated surface of an ocean, and by atmospheric turbulence; high-frequency ultrasound is scattered in polycrystalline metals and by dislocations in crystals. The propagation of sound in the atmosphere and in the ocean is affected by temperature and pressure distribution and by the force and velocity of the wind. These factors cause bending of the sound rays—that is, refraction—which in particular accounts for the fact that sound is audible farther with the wind than against it. The distribution of the speed of sound with depth in the ocean explains the existence of the so-called underwater sound channel, in which extremely long-range sound propagation is observed: for example, the sound of an explosion propagates for more than 5,000 km.

The second group of factors determining sound attenuation is associated with the physical processes in a substance, including the irreversible transformation of sound energy into other forms, mainly heat—that is, the absorption of sound, which is caused by the viscosity and thermal conductivity of the medium (“classical absorption”)—and the transformation of sound energy into the energy of intramolecular processes (molecular or relaxation absorption). Sound absorption increases markedly with frequency. Therefore, high-frequency ultrasound and hypersound usually propagate only over very short distances, most often no more than several centimeters. Infrasonic waves, which are distinguished by low absorption and weak scattering, are propagated the farthest in the atmosphere, in water, and in the earth’s crust. At high ultrasonic and hypersonic frequencies additional absorption occurs in solids as a result of the interaction of the waves with the thermal vibrations of the crystal lattice, with electrons, and with light waves. Under certain conditions this interaction can produce “negative absorption,” or the amplification of sound waves.

The importance of sound waves, and consequently their study (in acoustics), is extremely great. Since ancient times, sound has served as a means of communication and signaling. The study of all of its characteristics has made possible the development of more advanced data transmission systems, an increase in the range of signaling systems, and the creation of improved musical instruments. Sound waves are virtually the only form of signals that propagate in water, where they are used for submarine communications, navigation, and echolocation. Low-frequency sound is a tool for the study of the earth’s crust. The practical application of ultrasound has created ultrasonics, an entire branch of modern technology. Ultrasound is used for monitoring and measurement (particularly in flaw detection), as well as for operations on substances (ultrasonic cleaning, mechanical treatment, and welding). High-frequency sound waves, particularly hypersound, are an important means for research in solid-state physics.


Strutt, J. (Lord Rayleigh). Teoriia zvuka, 2nd ed., vols. 1–2. Moscow, 1955. (Translated from English.)
Krasil’ nikov, V. A.Zvukovye i ultrazvukovye volny v vozdukhe, vode i tverdykh telakh, 3rd ed. Moscow, 1960.
Rozenberg, L. D. Rasskaz O neslyshimom zvuke. Moscow, 1961.



An alteration of properties of an elastic medium, such as pressure, particle displacement, or density, that propagates through the medium, or a superposition of such alterations; sound waves having frequencies above the audible (sonic) range are termed ultrasonic waves; those with frequencies below the sonic range are called infrasonic waves. Also known as acoustic wave; sound wave.
The auditory sensation which is produced by these alterations. Also known as sound sensation.


An oscillation in pressure of the atmosphere which is capable of being detected by the human ear.


a. a periodic disturbance in the pressure or density of a fluid or in the elastic strain of a solid, produced by a vibrating object. It has a velocity in air at sea level at 0°C of 331 metres per second (741 miles per hour) and travels as longitudinal waves
b. (as modifier): a sound wave
2. the sensation produced by such a periodic disturbance in the organs of hearing
3. Slang music, esp rock, jazz, or pop


1. Law (of a title, etc.) free from defect; legally valid
2. Logic
a. (of a deductive argument) valid
b. (of an inductive argument) according with whatever principles ensure the high probability of the truth of the conclusion given the truth of the premises
c. another word for consistent


Med an instrument for insertion into a bodily cavity or passage to dilate strictures, dislodge foreign material, etc.


1. a relatively narrow channel between two larger areas of sea or between an island and the mainland
2. an inlet or deep bay of the sea
3. the air bladder of a fish


the. a strait between SW Sweden and Zealand (Denmark), linking the Kattegat with the Baltic: busy shipping lane; spanned by a bridge in 2000. Length: 113 km (70 miles). Narrowest point: 5 km (3 miles)




An inference system A is sound with respect to another system B if A can only reach conclusions which are true in B. A type inference system is considered sound with respect to a semantics if the type inferred for an expression is the same as the type inferred for the meaning of that expression under the semantics.

The dual to soundness is completeness.
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