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We report an experimental study of magnetic-field-sensitive multi-wave interference, realized in a three-wave RF-atom system. In the F = 1 hyperfine level of the 87 R b 5 2 S 1 / 2 ground state, Ramsey fringes were observed via the spin-selective Raman detection. A decrease in the fringe contrast was observed with increasing free evolution time. The maximum evolution time for observable fringe contrasts was investigated at different atom temperatures, under free-falling and trapped conditions. As the main interest of the Ramsey method, the improvement in magnetic field resolution is observed with an increase of evolution time T up to 3 ms and with the measurement resolution reaching 0.85 nT. This study paves the way for precision magnetic field measurements based on cold atoms.