In this paper, we investigate the influence of an airfoil pitching frequency (reduced frequency) on dynamic stall behavior of a NACA0012 airfoil oscillating in a turbulent wake with Direct Numerical Simulations. The presence of an upstream turbulence with dynamically oscillated blades and airfoils is associated with the ambient flow unsteadiness and is encountered in many operating conditions. We have recently developed a methodology that allows us to study the effects of wake turbulence on an oscillating airfoil with high-fidelity moving overlapping grid approach in high-order numerical formulation. The turbulent wake is generated by a small solid cylinder placed upstream of an oscillating airfoil, and the vortices shed from the upstream cylinder interfere with the pitching airfoil dynamics that alters the dynamic stall characteristics. In this paper, we study how the effects of the wake turbulence on the dynamic stall change when the reduced frequency is changed. We compare two reduced frequencies for the airfoil oscillation, k = 0:16 and 0:25, and document the corresponding flow-fields and aerodynamic coefficients. We focus on understanding how the vortex dynamics change in different cases and how it effects the airfoil aerodynamic characteristics.