A wave's group velocity is one of its most important properties.  It characterizes the speed at which signals can be transmitted.  For waves traveling in a material medium, the group velocity is generally given by the differential slope of the dispersion relation (wave frequency versus wavevector).  However, for resonant or strongly scattering media, this formula breaks down.  In such media the prediction of group velocity thus became a classical problem in the study of waves.  In collaboration with experimentalists at the University of Manitoba and University of Pennsylvania, we have proposed a solution to this classical problem through the use of a "spectral function approach" [1].  In particular, the experimental results on the sonic group velocity, obtained by using the phase averaging method, exhibited very large and peculiar variations which break the theoretical bounds of the so-called effective medium theories, valid in the long wavelength regime.  With no adjustable parameters, the spectral function approach can quantitatively explain all the measured results.  The physical picture which emerges is that in strongly scattering media, wave multiple scattering can lead to a renormalization of the perceived medium property, which in turn can mean a "new" dispersion relation from which the group velocity should be calculated.

(1) "Group Velocity in Strongly Scattering Media", J. H. Page, P. Sheng, H. P. Schriemer, I. Jones, X. Jing, and D. A. Weitz, Science 271, 634 (1996).