29 pages, 11 figures.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], http://hdl.handle.net/10261/5490. 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.K. L. is supported by a Ramón y Cajal contract. S.M. is supported by an FPI 01/0728/2004 grant from Comunidad de Madrid. I.A. is supported by grant BES-2007-16830. I.A., K. L. and S.M. are supported in part by the Plan Nacional de Altas Energías FPA-2006-05485, FPA-2006-05423 and EC Commission under grant MRTN-CT-2004-005104.