We consider a family of solutions to string theory which depend on arb
itrary functions and contain regular event horizons. They describe six
-dimensional extremal black strings with traveling waves and have an i
nhomogeneous distribution of momentum along the string. The structure
of these solutions near the horizon is studied and the horizon area co
mputed. We also count the number of BPS string states at weak coupling
whose macroscopic momentum distribution agrees with that of the black
string. It is shown that the number of such states is given by the Be
kenstein-Hawking entropy of the black string with traveling waves.