  The effects of group and phase velocity mismatch are well-known in optical
harmonic generation, but the non-degenerate cases remain unexplored. In this
work we develop an analytic model which predicts velocity mismatch effects in
non-degenerate triple sum-frequency mixing, TSF. We verify this model
experimentally using two tunable, ultrafast, short-wave-IR lasers to
demonstrate spectral fringes in the TSF output from a 500 $\mu$m thick sapphire
plate. We find the spectral dependence of the TSF depends strongly on both the
phase velocity and the group velocity differences between the input and output
fields. We define practical strategies for mitigating the impact of velocity
mismatches.
