Av. Potapov et Cs. Campbell, PROPAGATION OF ELASTIC-WAVES IN DEEP VERTICALLY SHAKEN PARTICLE BEDS, Physical review letters, 77(23), 1996, pp. 4760-4763
A wave traveling upward through a particle bed is observed to steepen
and form a shock as the surface is approached. This steepening is due
to the increase in the local speed of sound that is induced by the loc
al pressure increase in the upward moving phase of the wave behind the
wave front. The pressure increase leads to an increase in the local c
oordination number which in turn increases the local elastic modulus a
nd the sound speed.