Spatial Patterns of Sound Propagation in Sand

This paper addresses the problem of how sound propagates in a granular medium composed of noncohesive particles. This propagation has many unusual aspects which are due to the fragile nature of the contacts between grains. Sound propagation in a granular material is very sensitive to the exact position of each of the grains. The thermal expansion of a single bead of about 3000 \AA{} can produce a change as large as 25% in the total transmission of the sound even though this expansion is 4 to 5 orders of magnitude smaller than the wavelength of the sound or the size of a bead (5 mm). I interpret this as being due to sound propagating predominantly along force chains within the medium. By replacing some of the beads with local heaters, I have used this effect to investigate the spatial properties of the low-amplitude vibrations. The disturbance of a single heater can be characterized by a time scale ${\mathrm{\ensuremath{\tau}}}_{\mathit{h}}$ which reveals the elapsed time of the signal traveling along a path via the heater. Two heaters placed symmetrically with respect to the source and detector can produce very different disturbances. Finally, I show that the spatial pattern caused by heaters placed at different positions within the medium is very irregular in that two adjacent heaters can give very different responses. These experiments all indicate the presence of strong inhomogeneities and the existence of force chains within the medium along which the sound predominantly travels.