The interaction Hamiltonian of a two-level atom and a single-mode radiation field with time-varying frequency is analysed. The special attention is paid on the relationship between the atom-field coupling and frequency of cavity field or volume of cavity. By using vibration mechanism of cavity mirror, the impact induced by vibration of cavity mirror on the optical mode inside the cavity and volume of cavity is studied, and the exact relationship between the time-varying frequency of cavity field and atom-field coupling constant is found.