The quantum spin Hall effect (QSHE) has attracted much attention from both theoretical and experimental aspects.First principles calculations predicted that the low-buckled silicene and germanene are the promising candidates for QSHE.We theoretically investigated two kinds of density oscillations, the Friedel oscillations and collective excitation in the silicene and germanene within the random phase approximation.We found that the tunable spin-valley coupled band structure could lead to some exotic properties in these two phenomena.Based on an exact analytical and numerical analysis, we demonstrated that the beating of screened potential as well as the undamped plasmon mode can be taken as fingerprints of a topological phase transition in doped silicene and doped germanene.Our proposal could establish the connection between the topological phase transition and the density oscillations that can be accessed by a variety of experimental techniques.