chapter  48
Acoustic Measurement
Pages 24

Sound is normally deŸned as vibration of a solid, liquid, or gaseous medium in the frequency range of the human ear, that is, between about 20 Hz and 20 kHz. Here, the deŸnition is further limited and only vibrations in liquid and gaseous media are considered. In contrast to solid media, a liquid or gaseous medium cannot transmit shear forces, so sound waves are always longitudinal waves, in which the particles move in the direction of propagation of the wave. œe wave propagation in gaseous and liquid media can be described by the three variables: the pressure p, the particle velocity u, and the density ρ. œe relation between these is described by the wave equation [1], and this can be derived from three basic equations: the Euler equation (this is essentially Newton’s second law applied to a žuid), the continuity equation, and the state equation. Although the wave equation, in principle, can be used to describe and calculate all sound waves in all situations, it will in practice o£en be impossible to perform the necessary calculations. In some special cases, it is possible to get analytical results directly from the wave equation, and these cases are therefore of special interest. œe cases most o£en encountered in acoustics are the free ¥eld, the di–use (or reverberant) ¥eld, and the closed coupler. œe free Ÿeld is, in principle, an inŸnite, empty (except for the medium and the source) space, with no režections. Here, the waves are allowed to radiate freely in all directions without režections. In practice, the free Ÿeld is implemented in anechoic chambers, where all walls have been made nearly 100% absorptive. œe di¥use Ÿeld is obtained in a reverberation room where all walls have been made, in principle, 100% režective. At the same time, the walls are made nonparallel and the result is a sound Ÿeld with sound waves in all directions. œe closed coupler is a small chamber, with dimensions small compared to the wavelength of the sound. A special case of this is the standing wave tube. œis is a tube with a diameter smaller than the wavelength and with a sound source in one end. With a suitable loudspeaker as a source, the wave propagation in the tube can be assumed to be 1-D. œis simpliŸes the mathematical description so that it is possible to calculate the sound Ÿeld.