The fate of particles continuously injected at a fixed location in the vicinity of an oscillating front is studied by numerical integration of the hydrodynamic equations. The analysis is straightforward when the injection is at a location that is always on one side of the front. In this case, the curve traced by these particles, i.e., a streak line, may be complicated and generally does not resemble the path of the initial particle release, but at least is continuous. However, when the front oscillates across the source location, the streak line is broken into a series of discontinuous segments. Moreover, some segments later may recirculate past the source. This can produce a complicated streak line pattern in which old segments intertwine with recent segments.