Sound Propagation

Force chains are responsible for many of the unusual properties of the granular media such as the depth-independence of the pressure inside the material, or the absorption of sound. For example: because the pressure at the bottom of the upper compartment in an hour glass does not depend on the filling height, the flow rate is, to fairly good approximation, independent of time. This is very much different from what we would expect from a liquid (imagine an hourglass filled with water) and is the reason why hour glasses have been used as linear time measurement devices for centuries. What about sound transmission in a granular material? (Remember that sand is often used for sound and/or vibration absorption.) Sound cannot propagate uniformly through the medium, but has to travel along the tenuous connections that make up the force chains, splitting up and possibly reconnecting at various points. Consequently, if one initiates a sound wave at one point in the material, the transmitted signal at a second position is dramatically sensitivity to the exact arrangement of all the particles in the container. This extraordinary sensitivity is shown in the data below:

data on sound transmission sensitivity

In this figure, Ad is the acceleration (in units of the Earth's acceleration, g) sensed by detector D2, as a function of time, t. S is the sound source (continuous excitation with a sine wave), detector D1 monitors the source excitation to keep it constant via a feedback circuit, and H denotes a small heater element, the size of one of the glass beads, about 2mm diameter, located off-axis. At 20s and, again, at 105s the heater is turned on, raising the local bead temperature by only 1 degree Celsius. The resulting thermal expansion is sufficient to disturb the local force chains enough to cause a 50% drop in transmitted acceleration!