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The dispersion relation is derived for the coherent waves in fluid or elasticmedia supporting viscous and thermal effects and containing randomlydistributed spherical scatterers. The formula obtained is the generalization ofLloyd and Berry's [Proc. Phys. Soc. Lond. 91, 678-688, 1067], the latter beinglimited to fluid host media, and it is the three-dimensional counterpart ofthat derived by Conoir and Norris [Wave Motion 47, 183-197, 2010] forcylindrical scatterers in an elastic host medium.

Effective wave numbers for thermo-viscoelastic media containing random configurations of spherical scatterers