Solar transients impinging on Earth’s magnetosphere often present a larger velocity than the surrounding solar wind, leading to a different response of the bow shock-magnetosheath system. As such, we intend to provide a systematic study of the global effects of different solar wind Mach numbers in a pure quasi-perpendicular configuration with a realistic three-dimensional terrestrial-like curved bow shock. Simulations have been performed with the hybrid code LatHyS, which is based on the widely used CAM-CL scheme. In particular, we have studied the interaction with the terrestrial magnetosphere of a solar wind at different Alfvénic Mach numbers and low-beta (less than unity, ratio between the thermal to the magnetic pressures). One of most noteworthy outcome is the generation of an intense rippling phenomenon propagating along the bow shock surface as the incoming Mach number increases. A similar rippling has been observed in-situ with satellites, as well as studied with computer simulations. However, the latter have mainly addressed by adopting ad-hoc planar-shock initial configurations, which still leaves poor knowledge of the possible effects on a global three-dimensional curved interaction. Our analysis then is expected to provide further insights into both the macroscopic and kinetic effects of different incoming solar wind conditions on the overall planetary bow-shock and magnetosheath structure.