The problem of earthquake triggering by dynamic stress waves is studied. A finite fault of length L embedded in an elastic space is considered. The prescribed nonlinear slip-dependent friction law is characterized by a nonconstant weakening rate α. The fault is perturbed by a sinusoidal stress wave of wavelength λ and amplitude a. As a general result, it is shown that for a given fault and a given friction law, low frequencies are more likely to trigger the rupture than high frequencies. In addition, the occurrence of triggering depends on the balance between intrinsic fault mechanics and the loading parameters. Two behaviors are possible depending on the friction law: some faults exhibit a threshold in frequency to be triggered, while other faults exhibit a threshold in amplitude. These two qualitative behaviors may be explained by considering the nondimensional weakening rate ¿ = α ¿ L/2 and ¿0 the universal constant of stability computed by Dascalu et al. <2000>. The faults that present a threshold in frequency are intrinsically unstable: their initial nondimensional weakening rate ¿(0) exceeds ¿0. On the contrary, the faults that present a threshold in amplitude are intrinsically stable, i.e., initially ¿(0) < ¿0. Because of the nonlinearity of the friction law, there is a characteristic slip uc for which ¿(uc) ≥ ¿0. For a sufficiently large amplitude the fault may then experience a stability/instability transition. These results are independent of the shape of the perturbation and also hold for a static stress increase.