  We continue our investigations on the relation between hydrodynamic and
higher quasinormal modes in the AdS black hole background started in
arXiv:0710.4458 [hep-th]. As is well known, the quasinormal modes can be
interpreted as the poles of the retarded Green functions of the dual N=4 gauge
theory at finite temperature. The response to a generic perturbation is
determined by the residues of the poles. We compute these residues numerically
for energy-momentum and R-charge correlators. We find that the diffusion modes
behave in a similar way: at small wavelengths the residues go over into a form
of a damped oscillation and therefore these modes decouple at short distances.
The sound mode behaves differently: its residue does not decay and at short
wavelengths this mode behaves as the higher quasinormal modes. Applications of
our findings include the definition of hydrodynamic length and time scales. We
also show that the quasinormal modes, including the hydrodynamic diffusion
modes, obey causality.
