Scattering by random distribution of spheres vs. concentration

We give data and theory for scattering of 5-mm waves by Styrofoam spheres moving randomly within a slab region Styrofoam container. The results summarize two systematic programs of measurements for the forward scattered coherent phase, the average intensities (coherent, incoherent, and total), and for the variances and covariance of phase-quadrature components of the instantaneous field. These were obtained separately and simultaneously vs. the number ( ) of spheres in the container for concentrations corresponding to sparse gases through dense gases, on to the limiting case of an amorphous solid. Two relatively distinct "compression processes" for which the coherent phase increased linearly with increasing were studied: the amplitude of the covariance was either as large or as small as we could obtain. The data records for the small case are in relatively good accord with computations; those for the large show departures in the direction indicated by qualitative considerations of the effects of clumping.