Motivated by recent observations which detect an outer boundary for starless cores, and evidence for time-dependent mass accretion in the Class 0 and Class I protostellar phases, we reexamine the case of spherical isothermal collapse in the case of a finite mass reservoir. We show that the inward propagating rarifaction wave, which is caused by a finite mass reservoir of a collapsing cloud core, traces the conceptual border between the Class 0 and Class I protostellar evolutionary stages. The results were published in Monthly Notices of the Royal Astronomical Society, 2005, 360, 675. The poster (in Microsoft PowerPoint format) is accessable here. The paper in the pdf format can be downloaded here . This research was done in collaboration with Prof. Shantanu Basu.