A response variation (RV) element is introduced to control the consistency of the wideband beamformer's response over the frequency range of interest at the look direction. By constraining the value of RV in different ways, we develop two novel adaptive wideband beamformers based on the traditional least mean square (LMS) adaptation and the convex optimization method, respectively. Both beamformers can achieve an improved output SINR compared to the conventional Frost beamformer due to their increased number of degrees of freedom in suppressing the interferences, as shown in simulations.