Sound propagation in a constrained lattice of beads: High-frequency behavior and dispersion relation

Abstract : We report on acoustic wave propagation in a regular array of nominally identical beads under isotropic static stress. The weak polydispersity of the beads makes the contact lattice random. Time-frequency analysis of the acoustic signal is performed and allows measurement of the full lattice dispersion relation. Comparison with the theoretical prediction for a perfect triangular lattice gives an indication of the level of randomness in the contact lattice. The results extend, in a consistent way, a previous study restricted to long wavelength propagation [B. Gilles and C. Coste, Phys. Rev. Lett. 90, 174302 2003 ] The contact lattice is ordered by increas- ing the stress, and the smaller the wavelength, the higher the stress required to get regular lattice behavior. Measurements involving ballistic propagation of the coherent wave, whatever its frequency, evidence revers- ible lattice behavior under compression and/or decompression. Nevertheless, correlations of short wavelength incoherent waves are a sensitive probe of disorder, and allow us to exhibit a small irreversible evolution of the lattice.
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Christophe Coste, Bruno Gilles. Sound propagation in a constrained lattice of beads: High-frequency behavior and dispersion relation. Physical Review E , American Physical Society (APS), 2008. ⟨hal-01406704⟩

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