Non-linear sound is an extreme phenomenon typically observed in solids after
violent explosions. But granular media are different. Right when they jam,
these fragile and disordered solids exhibit a vanishing rigidity and sound
speed, so that even tiny mechanical perturbations form supersonic shocks. Here,
we perform simulations in which two-dimensional jammed granular packings are
dynamically compressed, and demonstrate that the elementary excitations are
strongly non-linear shocks, rather than ordinary phonons. We capture the full
dependence of the shock speed on pressure and impact intensity by a
surprisingly simple analytical model.Comment: Revised version. Accepted for publication in Phys. Rev. Let