a region in space in which sound waves are propagating, that is, where acoustic vibrations of the particles of the solid, fluid, or gaseous elastic medium filling the region occur. A sound field is completely defined if for each of its points the temporal and spatial variation of any of the quantities that characterize a sound field—the displacement of a vibrating particle from its equilibrium position, the vibration velocity of a particle, or the sound pressure in the medium—is known; in certain cases, changes in the density or temperature of the medium in the presence of a sound field are of interest. The concept of a sound field is usually used for regions having dimensions on the order of, or greater than, the wavelength of the sound.

From the standpoint of energy, a sound field is described by the density of the sound energy, or by the energy of the vibratory process per unit volume; if energy transfer is occurring in the sound field, it is described by the sound intensity, which is the time average of the energy transferred per unit time through a unit of surface perpendicular to the direction of wave propagation.

The pattern of a sound field depends in general not only on the acoustic power and the directional characteristics of the radiator, or sound source, but also on the position and properties of the interfaces of the different elastic mediums, if any exist. In an infinite homogeneous medium the sound field is a traveling-wave field. Far from the source in the sound field of virtually any radiator the sound pressure decreases according to the law 1/r, where r is the distance from the source. The superimposition of two sound waves of equal amplitude that are moving toward each other produces a standing-wave field; in a more general case, the sound fields of traveling and standing waves are superimposed on one another. In closed spaces a sound field may be diffuse—that is, a field in which all directions of the transfer of sound energy are equally probable because of the simultaneous presence of a great number of reflected waves moving in all possible directions. Sound fields are measured with microphones, hydrophones, acoustic probes, and other sound receivers. Methods of sound field visualization may be used to study sound fields of complex shape. The sound fields of various radiators are studied in anechoic chambers.