  We construct boundary states for D-branes which carry traveling waves in the
covariant formalism. We compute their vacuum amplitudes to investigate their
interactions. In non-compact space, the vacuum amplitudes become trivial as is
common in plane wave geometries. However, we found that if they are
compactified in the traveling direction, then the amplitudes are affected by
non-trivial time dependent effects. The interaction between D-branes with waves
traveling in the opposite directions (`pulse-antipulse scattering') are also
computed. Furthermore, we apply these ideas to open string tachyon condensation
with traveling waves.
