Diffuse ultrasonic transport in an unconsolidated glass bead pack

We study the transport of diffuse ultrasound with frequencies of hundreds of kHz through random aggregates of d = 3.0 and 1.0 mm diameter spherical glass beads in air under static loads of 100 to 300 kPa. Highdensity polystyrene foam on top and bottom transmits the static loads while maintaining ultrasonic isolation. A floating polystyrene foam wall helps establish a uniform hydrostatic load through the 10 to 70 mm depths. Findings include a band gap extending—for the 3 mm beads—from a lower edge at about 200 kHz (that scales weakly with load and inversely with bead diameter.) Amongst the 3mm beads, we observe an upper edge to the band gap at about 900 kHz corresponding to an optical branch passband associated with the lowest internal resonance of an isolated bead. Higher optical branches are observed also. The lower edge at 200 kHz corresponds well with estimates of the upper band edge for the rotational-wave vibrations of a hexagonal close packed array of beads in Hertzian contact. The observed first arrival times correspond well with Hertzian predictions for low frequency effective longitudinal wavespeeds. Within the low frequency pass band we see diffuse transport, with diffusivities comparable to simple theoretical expectations.