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(əko͞o`stĭks) [Gr.,=the facts about hearing], the science of soundsound,
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, and architectural acoustics. Unlike electromagnetic radiationelectromagnetic radiation,
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, which can travel in the vacuum of free space, sound WavesWaves
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 require a medium (solid, liquid, or gas) in which to travel. Another important difference is that sound travels much slower than electromagnetic radiation; the speed of sound in air at sea level is approximately 1000 ft/sec (300 m/sec), which is roughly a millionth the speed of light in air. Sound waves are longitudinal, which means that the material particles transmitting the waves oscillate in the direction of propagation. Important factors to be considered in working with sound include reverberation and interferenceinterference,
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. Reverberation is the persistence of sound in an enclosed space caused by repeated reflections. Reflection of sound sometimes causes an echoecho,
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. Depending on the location of the listener and the frequency of the sound, varying degrees of interference between the primary sound and its reflections will be produced. Reflection can be reduced by the use of sound-absorbent materials, which are usually soft and porous, such as draperies, upholstery, carpets, acoustic tile, or plaster. In a room, reflection is decreased by the presence of people and open windows and doors.


See J. Backus, The Acoustical Foundations of Music (1969); R. B. Lindsay, Acoustics (1973); A. D. Pierce, Acoustics (1981, repr. 1989).



The science of sound, which in its most general form endeavors to describe and interpret the phenomena associated with motional disturbances from equilibrium of elastic media. An elastic medium is one such that if any part of it is displaced from its original position with respect to the rest, as for example by an impact, it will return to its original state when the disturbing influence is removed. Acoustics was originally limited to the human experience produced by the stimulation of the human ear by sound incident from the surrounding air. Modern acoustics, however, deals with all sorts of sounds which have no relation to the human ear, for example, seismological disturbances and ultrasonics.

Basic acoustics may be divided into three branches, namely, production, transmission, and detection of sound. Any change of stress or pressure producing a local change in density or a local displacement from equilibrium in an elastic medium can serve as a source of sound. Transmission of sound takes place through an elastic medium by means of wave motion. The most important sound waves are harmonic waves, defined as waves for which the propagated disturbance at any point in its path varies sinusoidally with time with a definite frequency or number of complete cycles per second (the unit being the hertz). Acoustics deals with waves of all frequencies, but not all frequencies are audible by human beings, for whom the average range of audibility extends from 20 to 20,000 Hz. Sound below 20 Hz is referred to as infrasonic, and that above 20,000 Hz is called ultrasonic.

The detection of sound is made possible by the incidence of transmitted sound energy on an appropriate acoustic transducer, such as the ear. For modern applied acoustics, transducers such as the microphone, based on the piezoelectric effect, are widely used. Generally speaking, any transducer used as a source of sound is also available as a detector, though the sensitivity varies considerably with the type.




literally, the study of sound—that is, of elastic vibrations and waves in gases, liquids, and solids audible to the human ear with frequencies in the range of 16 Hz to 20 kHz; in the broad sense, the field of physics that investigates elastic vibrations and waves from the lowest frequency (conventionally 0 Hz) to maximum frequencies of 1012 to 1013 Hz, their interactions with matter, and the applications of these vibrations (waves).

Historical survey. Acoustics, one of the most ancient fields of knowledge, grew out of the need to provide an explanation for the phenomena of hearing and speech, and especially of musical sounds and instruments. The Greek mathematician and philospher Pythagoras (as early as the sixth century B.C.) discovered the correlation between the pitch of a tone and the length of a string or pipe; Aristotle (fourth century B.C.) concluded that a sounding body produced compressions and rarefactions of the air and explained an echo as the reflection of sound from an obstacle.

The Middle Ages contributed little to the development of acoustics; substantial progress began in the Renaissance. The Italian scientist Leonardo da Vinci (15th and 16th centuries A.D.) investigated the reflection of sound and formulated the principle of the independence of sound waves propagated from different sources.

The historical development of acoustics as a physical science can be divided into three periods. The first period, from the beginning of the 17th century to the beginning of the 18th century, is characterized by investigations of musical tone systems, their sources (strings and pipes), and the propagation velocity of sound. Galileo discovered that a sound-producing body was vibrating and that the pitch of the sound depended on the frequency of these vibrations while the intensity of the sound depended on their amplitude. The French scientist M. Mersenne, following Galileo, was able to measure the number of vibrations of a resonant string; he was the first to measure the velocity of sound in air. R. Hooke (England) established experimentally the proportionality between the strains in a body and the associated stresses, a fundamental law of the theories of elasticity and of acoustics; and C. Huygens (Holland) established the very important principle of wave motion which is named after him.

The second period covers two centuries, from the establishment of the principles of mechanics by I. Newton (the end of the 17th century) up to the beginning of the twentieth century. During this period acoustics developed as a division of mechanics. A general theory was established for mechanical vibrations and the radiation and propagation of sound (elastic) waves in a medium; methods were developed for measuring the properties of sound: sound pressure in a medium, momentum, the energy and the energy flow of sound waves, and the propagation velocity of sound. The range of sound waves was broadened to cover both the infrasonic (below 16 Hz) and the ultrasonic (above 20 kHz) regions. The physical significance of sound timbre (its “coloration”) was explained.

Classical physics started to flourish with Newton’s work. Mechanics, hydrodynamics, the theory of elasticity, and the theory of waves, both acoustic and optical, were developed in close association with one another. L. Euler and D. Bernoulli, who were members of the St. Petersburg Academy of Sciences, and the French scientists J. D’Alembert and J. Lagrange developed the theory of vibrating strings, rods, and reeds, and accounted for the origin of overtones. The German scientist E. Chladni (late 18th to early 19th centuries) experimentally investigated the shapes of vibrations produced by sounding bodies including membranes, plates, and bells. T. Young (England) and A. Fresnel (France) developed Huygens’ ideas on wave propagation and created the theory of wave diffraction and interference. C. Doppler (Austria) established the law for the change in frequency of a wave as the sound source moves with respect to the observer. Of great significance, not only for acoustics but for physics as a whole, was the advent of methods for breaking down a complex vibratory process into simple components—the analysis of vibrations—and the synthesis of complex vibrations from the simple components. A mathematical method of expanding periodically recurring processes into simple harmonic components was discovered by the French scientist J. Fourier. The experimental analysis of sound, the separation into a spectrum of harmonic vibrations with a set of resonators, and the synthesis of a complex sound from simple components was accomplished by the German scientist H. Helmholtz. Using a set of tuning forks with resonators, Helmholtz was able to reproduce artificially different vowel sounds. He investigated the composition of musical sound and explained the timbre of a sound as a set of additional tones (harmonics) that characterize it. On the basis of his theory of resonators, Helmholtz formulated the first physical model of the ear as an acoustic apparatus. His investigations laid a basis for physiological acoustics and musical acoustics. This stage of the development of acoustics was summed up by the English physicist Lord Rayleigh (J. Strutt) in his classic treatise “The Theory of Sound.”

In Russia at the turn of the 20th century, important work was carried on by the physicist N. A. Umov, who introduced the concept of energy flow for elastic waves. The American scientist W. C. Sabine laid the foundations of architectural acoustics. The Russian physicist P. N. Lebedev (along with N. P. Neklepaev) isolated from the sharp sound of an electric spark the ultrasonic waves having frequencies up to several hundred kHz and investigated their absorption in air.

In the early 20th century interest in acoustics declined; it was considered to be a theoretically and experimentally complete scientific field, with only special types of problems remaining unsolved.

The third, modern period in the history of acoustics, which began in the 1920’s, is associated first of all with the development of electroacoustics and the advent of radio technology and radio broadcasting. A new area of problems arose in acoustics—the conversion of acoustic signals into electromagnetic signals and the reverse, their amplification and undistorted reproduction. At the same time, radiotech-nology and electroacoustics revealed previously unknown possibilities for acoustical developments. Electroacoustics appeared as far back as the last quarter of the 19th century. The telephone was invented in 1876 (Bell, USA) and the phonograph in 1877 (Edison, USA). In 1901 magnetic sound recording was developed and later was used in the tape recorder and in sound motion pictures. At the beginning of the 20th century electromechanical sound transducers were employed in loudspeakers, and in the 1920’s they became the basis for all modern acoustic apparatus.

The electron tube made it possible to amplify extremely weak acoustic signals that had been converted into electric signals. Methods were developed for making radioacoustic measurements, analyzing sound, and reproducing it. These new possibilities revolutionized acoustics, transforming what was regarded as a completed department of mechanics into an independent division of modern physics and technology.

Acoustics development received a great impetus during the first half of the 20th century in connection with military technical problems. The problem of determining the position and velocity of an aircraft (radar) and of a submarine (sonar); determining the location, time, and nature of an explosion; muffling aircraft noises—all these problems required deeper study of the mechanisms by which sound is created and absorbed, and of the propagation of sound waves (particularly ultrasonic waves) under complex conditions. The problems of sound generation became the object of extensive investigations in association with the development of a general theory of oscillations which covered jointly mechanical, electrical, and electromechanical oscillatory processes. In the 1920’s and 1930’s many articles were devoted to the theory of self-oscillations, the self-sustaining oscillations in a system associated with a constant source of energy; a large contribution to the development of this theory was made by the Soviet school of physics headed by L. I. Mandel’shtam and N. D. Papaleksi. There was particular interest in the question of high-intensity sound wave propagation (for example, of explosive waves); the works of the Russian physicists A. A. Eikhenval’d and N. N. Andreev in this field were major contributions to nonlinear acoustics, which has as its objective the study of high-power sound fields. M. Lighthill (England, 1952) gave a general theory of aerodynamic sound generation, studying the origin of sound in a moving medium due to instability of the gas flow. N. N. Andreev and I. G. Rusakov (1934) and D. I. Blokhintsev (1947) developed the fundamentals of the acoustics of moving media.

The first advances in sonar were made by the French physicist P. Langevin (1916), who employed ultrasonic waves to measure the depth of the sea and to detect submarines. The phenomenon of very-long-range propagation of sound from an explosion in the sea along submarine acoustic channels was discovered independently by American scientists (M. Ewing and J. Worzel, 1944) and Soviet scientists (L. M. Brekhovskikh and L. D. Rozenberg, 1946). The problems of sound absorption and sound dissipation, which are of special importance in the development of architectural and building acoustics, were investigated by S. N. Rzhevkin, G. D. Maliuzhinetz, and V. V. Furduev. Great attention has been devoted to the study of acoustical noises and methods of eliminating them.

The study of the effect of a medium’s structure on sound propagation in turn opened up the possibilities of employing sound waves to probe the medium (in particular, the atmosphere); this led to the development of atmospheric acoustics.

During the last two decades ultrasonics research has become very important. Special study is devoted to high frequencies and high intensities, which offer a means of studying the structure and properties of substances. As early as the 1920’s, Soviet scientist S. Ia. Sokolov utilized ultrasound as a flaw detector for metals. In Germany, H. O. Kneser (1933) discovered the phenomenon of strong ultrasonic absorption and dispersion in polyatomic gases. Later the dispersion and anomalous absorption of ultrasound was also observed in liquids. A general theory of these phenomena—that is, relaxation theory—was given by L. I. Mandel’shtam and M. A. Leontovich (1937). Ultrasonic vibrations of high frequency also cause a rearrangement of the structure in liquids, dissociation of the molecules, and many other effects. Linking acoustics and optics, Mandel’shtam (1918 and 1926) and L. Brillouin (France, 1922) originated the theory of light scattering by ultrasonic waves in liquids and solids. This phenomenon has proved to be important for studying the molecular structure of substances.

The range of questions associated with the effect of a substance’s molecular structure on ultrasonic propagation is called molecular acoustics, which is the study of ultrasonic absorption and dispersion in polyatomic gases, liquids, and solids. Ultrasound has turned out to be not only a method of investigation but also a powerful tool for acting on a substance.

The investigation of hypersound (frequencies of 1 gigahertz and higher) has become very important. The interaction between hypersonic waves and electrons in metals and semiconductors has been studied intensively.

Great changes have taken place in the old subdivisions of acoustics. In the middle of the 20th century psychophysiological acoustics started to develop rapidly, stimulated by the need to have methods of transmitting and reproducing, without distortion, a multitude of acoustic signals, such as speech and music, over a limited number of communication channels. These acoustics problems are included in the scope of problems in the general theory of information and communication. Studies were made of the mechanisms by which different speech sounds are produced, the nature of their sound spectra, and the basic factors involved in speech quality and hearing perception. Instruments were developed to make speech visible, thus providing a visual image of the various sounds. Methods were developed for coding speech (compressed transmission of its basic elements) and for decoding it (synthesis); investigations were expanded into the mechanisms of hearing perception, loudness sensation, and judgment of sound direction (the Hungarian scientist G. von Békésy). In this field acoustics joined forces with the physiology of the organs of sensation and with biophysics.

Thus, in its content and knowledge, modern acoustics has gone far beyond the boundaries within which it had developed before the 20th century.

The fundamental divisions of acoustics. Modern acoustics is subdivided into general, applied, and psychophysiological acoustics.

General acoustics is concerned with theoretical and experimental studies of the laws governing the radiation, propagation, and reception of elastic vibrations and waves in various media and systems; it can be arbitrarily divided into the theory of sound, physical acoustics, and nonlinear acoustics. The theory of sound makes use of the general methods developed in vibration and wave theory. For vibrations and waves of small amplitude, use is made of the principle of independence of the vibrations and waves (the superposition principle). On this basis a sound field in various regions of space and also its variation with time are defined.

A great number of factors associated with the properties and state of a medium have been shown to affect the propagation, generation, and reception of elastic waves. This is the concern of physical acoustics. Outstanding among its problems is the study of elastic wave velocity and absorption as a function of the temperature and viscosity of the medium and other factors.

The interactions of elementary sound waves (phonons) with electrons and photons are also regarded as being among the important problems of physical acoustics. These interactions become especially important at very high ultrasonic and hypersonic frequencies for low temperatures. In these temperature and frequency regions, quantum effects begin to appear. This division of physical acoustics is sometimes called quantum acoustics. Nonlinear acoustics deals with intense sound processes where the superposition principle is not applicable and a sound wave changes the properties of the medium while propagating. This division of acoustics, which has very complex theoretical relationships, is developing rapidly (as is the theory of nonlinear wave processes in optics and electrodynamics).

Applied acoustics is an extremely broad field which includes, first of all, electroacoustics. Also included are acoustic measurements—the measurement of sound pressure and intensity, the frequency spectrum of an acoustic signal, and the like. Architectural and building acoustics are concerned with the problems of ensuring good audibility for speech and music in enclosed spaces and with the reduction of noise levels, as well as with the development of sound-insulating and sound-absorbing materials. Applied acoustics also deals with noise and vibration and the development of means to control them. Hydroacoustics and hydrolocating occupy themselves with the study of sound propagation in the ocean and the resulting phenomena, such as the acoustic refraction and reverberation when an acoustic signal is reflected from the surface or bottom of the sea and the scattering of sound by heterogeneities.

Atmospheric acoustics investigates the characteristics of sound propagation in the atmosphere that are the result of its structural heterogeneity, and is a part of meteorology. Geoacoustics deals with the application of sound in engineering geophysics and geology.

Ultrasound and hypersound are of enormous practical value both in the technology of physical experimentation and in industry, transportation, medicine, and elsewhere. For example, measurement technology includes ultrasonic delay lines, measurement of the compressibility of liquids, the elastic modulus of solids, and the like; industrial control includes the detection of flaws in metals and alloys, monitoring the progress of chemical reactions, and so on; the technological applications include ultrasonic drilling, cleaning and treating surfaces, the coagulation of aerosols, and others.

Psychophysiological acoustics is the study of the sound-emitting and sound-detecting organs of man and animals, together with the problems of producing, transmitting, and reproducing speech. The results are utilized in electroacoustics, architectural acoustics, speech transmission systems, theories of information and communication, and in music, medicine, biophysics, and so forth. Among its divisions are: speech, hearing, psychological acoustics, and biological acoustics.

Problems in acoustics are being studied in Moscow at the Institute of Acoustics of the Academy of Sciences of the USSR, the Scientific Research Institute of Structural Physics, the Scientific Research Institute of Cinematography, and the Institute of Sound Recording; in Leningrad at the Institute of Radio Reception and Acoustics; and at a number of university departments and also at a large number of laboratories and chairs in the universities and colleges of the country.

The scientific problems of acoustics are dealt with in various physics journals as well as in special acoustic journals: Akusticheskii zhurnal (Moscow, since 1955), Acustica (Stuttgart, since 1951), Journal of the Acoustical Society (New York, since 1929), and others.


Rayleigh, J. W. S. Teoriia zvuka, 2nd ed. Moscow, 1955. (Translated from English.)
Skudryzk, E. Osnovy akustiki, vols. 1 and 2. Moscow, 1958–59. (Translated from German.)
Krasil’nikov, V. A. Zvukovye i ul’trazvukovye volny ν vozdukhe, vode, i tverdykh telakh, 3rd ed. Moscow, 1960.




The science of the production, transmission, and effects of sound.
The characteristics of a room that determine the qualities of sound in it relevant to hearing.


1. The science of sound, including the generation, transmission, and effects of sound waves.
2. The totality of those physical characteristics of an auditorium or room (such as the size and shape of elements on the walls or ceiling which scatter sound, the amount of sound absorption, and noise level within the room) which affect an individual’s perception, and judgment, of the quality of speech and music produced in the room.


1. the scientific study of sound and sound waves
2. the characteristics of a room, auditorium, etc., that determine the fidelity with which sound can be heard within it
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