Cavity flows are a prevalent phenomenon in aerospace engineering, known for their intricate structures and substantial pressure fluctuations arising from interactions among vortices. The primary objective of this research is to predict noise levels in high-speed cavity flows at Mach 4 for a rectangular cavity characterized by an aspect ratio of L/D = 7. Moreover, this study delves into the influence of the plasma actuator on noise control within the cavity flow regime. To comprehensively analyze acoustic characteristics and explore effective noise reduction strategies, a computational fluid dynamics technique with the combination of a delayed detached eddy simulation (DDES) and plasma phenomenological model is established. Remarkably, the calculated overall sound pressure level (OASPL) and plasma-induced velocity closely align with the experimental data, validating the reliability of the proposed approach. The results show that the dielectric barrier discharge (DBD) plasma actuator changes the movement range of a dominating vortex in the cavity to affect the OASPL at the point with the maximum noise level. The control of excitation voltage can reduce the cavity noise by 2.27 dB at most, while control of the excitation frequency can only reduce the cavity noise by 0.336 dB at most. Additionally, the increase in excitation frequency may result in high-frequency sound pressure, but the influence is weakened with the increase in the excitation frequency. The findings highlight the potential of the plasma actuator in reducing high-Mach-number cavity noise.