Contribution of plasma oscillation to the broadband terahertz (THz) emission is revealed by interacting two-color (ω/2ω) laser pulses with a supersonic jet of nitrogen molecules. Temporal and spectral shifts of THz waves are observed as the plasma density varies. The former owes to the changing refractive index of the THz waves, and the latter correlates to the varying plasma frequency. Simulation of considering photocurrents, plasma oscillation and decaying plasma density explains the broadband THz spectrum and the varying THz spectrum. Plasma oscillation only contributes to THz waves at low plasma density owing to negligible plasma absorption. At the longer medium or higher density, the combining effects of plasma oscillation and absorption results in the observed low-frequency broadband THz spectra.