energy is transmitted forward as a compaction wave
and part is reflected backward as a release wave. The release
wave, propagating at the local acoustic speed for the consolidated
solid, causes an imperceivable decrease in solid volume
fraction, significant decreases in solid density, pressure, and
temperature, and a significant increase in velocity.This velocity
increase supports the propagation of the transmitted steady
wave through the loose material at speed D_ = 513 m/s. The
speed of the transmitted wave is less than that of the lead
wave due to larger dissipation in compacting the material
from φfp to φ ≈ 0.937, but is overdriven with respect to
the piston speed up = 100 m/s. In the limit t → ∞, this
overdriven wave will be weakened due to multiply reflected
release waves from the piston surface.