Frequency locking to an external forcing frequency is a known phenomenon. In the auditory system, it results in a localized traveling wave, the shape of which is essential for efficient discrimination between incoming frequencies. An amplitude equation approach is used to show that the shape of the localized traveling wave crucially depends on the relative strength of additive vs. parametric forcing components; the stronger the parametric forcing the more asymmetric the response prole and the sharper the traveling-wave front. The analysis captures empirically observed regions of linear and nonlinear responses and highlights the significance of studying combined-forcing mechanisms for understanding sound discrimination.