Abstract: Driven granular
media constitute model systems in out-of-equilibrium statistical
physics. By assimilating the motions of granular particles to
those of atoms, by analogy, one can obtain macroscopic
equivalent of phase transitions. Here, we study fluid-like and
crystal-like two-dimensional states in a driven granular
material. In our experimental device, a tunable magnetic field
induces and controls remote interactions between the granular
particles. We use high-speed video recordings to analyse the
velocity fluctuations of individual particles in stationary
regime. Using statistical averaging, we find that the particles
self-organize into collective excitations characterized by
dispersion relations in the frequencywavenumber space. These
findings thus reveal that mechanical waves analogous to
condensed matter phonons propagate in driven granular media.
When the magnetic coupling is weak, the waves are longitudinal,
as expected for a fluid-like phase. When the coupling is
stronger, both longitudinal and transverse waves propagate,
which is typically seen in solid-like phases. We model the
dispersion relations using the spatial distribution of particles
and their interaction potential. Finally, we infer the elastic
parameters of the granular assembly from equivalent sound
velocities, thus realizing the spectroscopy of a granular
material.