In nonlinear optical (NLO) crystals, the selection of pump light wavelengths for the generation of terahertz (THz) waves is limited due to problems associated with coherence length, refractive index, and absorption by the crystal. Relaxation of this limitation would open up potential light sources for THz generation. One such solution, Cherenkov phase matching, removes the coherence length constraint. In this study, we attempted to generate THz waves from an NLO crystal using femtosecond pulses of various wavelengths. Specifically, 805-nm and 1560-nm femtosecond pulses were used to pump a prism-coupled LiNbO3 crystal. Broadband THz-wave generation and a THz-wave output proportional to the square of the pump light intensity were observed at both wavelengths. The generation of THz waves by prism-coupled Cherenkov phase matching was not limited by the wavelength of the pump light. Moreover, THz-wave generation at even greater intensities may be possible by optimizing the pump source and coupling to an NLO crystal.