This study examines the dynamic interactions of single and double bubbles in infinite liquid domains within hydrodynamic cavitation systems notably within a single-hole orifice-plate reactor. Critical parameters such as cavitation radius and implosion time are analyzed by solving the Rayleigh-Plesset and Keller-Miksis models for compressible fluids. This analysis is extended to multiple oscillations after the initial cavitation implosion has occurred. Furthermore, a numerical solution of both the Rayleigh-Plesset and Keller-Miksis models is employed to demonstrate the influence of key factors, including the polytropic index in single bubble systems and inter-bubble distances, along with secondary Bjerknes forces in double-bubble interactions. The findings highlight the significant impact of one bubble on the oscillations of neighbouring bubbles, resulting in substantial variations in the overall dynamics of the system.