Reverberation chambers used for acoustical measurements should have completely random sound fields. We denote by R the cross-correlation coefficient for the sound pressures at two points a distance r apart. R = 〈p1p2〉Av/(〈p12〉Av〈p22〉Av)12, where p1 is the sound pressure at one point, p2 that at the other, and the angular brackets denote long time averages. In a random sound field, R = (sinkr)/kr, where k = 2π/(the wavelength of the sound). An instrument for measuring and recording R as a function of time is described. A feature of this instrument is the use of a recorder's servomechanism to measure the ratio of two dc voltages. The results of correlation measurements in reverberant sound fields are given.

In a reverberant sound field, where at all points equal mean energy flows in all directions, it is shown that the sound energy is distributed into interference patterns the reflecting boundaries. Thus the mean energy density is not uniform at all points in the field. For a perfectly reflecting plane surface that is large compared with the wavelength, the interference pattern can be expressed as a mean squared sound pressure varying as (1 + sin2kx/2kx) where x is the distance from the surface and k is the wave number. Corresponding expressions are derived for the mean squared particle velocity and the mean energy density. The energy level at the surface is found to be 2.2 db higher than at points further away where the interference patterns are negligible. Similar expressions are derived for the interference patterns formed by two and three reflectors at right angles, as at the edges and corners of a room. The largest departure from uniformity occurs in a corner where the mean squared pressure is 9 db higher than at remote points. The effects of such interference patterns on transmission loss and reverberation room measurements are discussed briefly. The patterns are not much affected by the frequency band widths habitually used in room acoustics. Experimental confirmation of the theory is given.

Reverberant sound fields are used in several standard acoustical measurements, in which the sound field is sampled at different points. Here, the distributions of such sampled values are considered for the reverberant sound fields derived from different types of signal. It is shown that the values approach equality only where the field contains many frequency components simultaneously. For finite numbers of components, exact expressions in closed form are found for the distributions. For the field derived from a single frequency component, the values of mean-squared pressure follow a gamma distribution. For two or more frequency components of different mean amplitude, the distribution is related to a gamma distribution, and some computed values of it are given for the case of two components. Some experimental data are given. The results bear on the accuracy to be expected in reverberant field measurements.

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Continuing earlier work on this subject, a more rigorous discussion is given of the singular points of streamlines and the critical points of the stream function. The results for vortex and saddle points obtained earlier in piecemeal fashion and by way of examples are obtained systematically and by generally utilizing the applicable theory of differential equations and calculus. New results are also obtained. For example, a saddle point can occur when the phase of pressure and velocity differ by π/2, and in certain parts of the sound field, specifically inside a closed streamline, the number of vortex points and saddle points are related. Finally, the streamlines and singular point are considered for a discrete source: the line source.