We have investigated the properties of low-amplitude vibrations in dry unconsolidated granular materials. The velocity of sound can vary by a factor of 5 depending upon whether one measures either the arrival time of the rising edge of the pulse or the quantity analogous to the group velocity. If we increase the amplitude of the vibrations, we observe nonlinearity near the point at which we first see hysteretic behavior. This is interpreted as due to the presence of force chains. We also find frequency shifts in all of the features that characterize the transmission spectrum.

• Received 3 September 1993

DOI:https://doi.org/10.1103/PhysRevB.48.15646