In quantum dots made from materials with nonzero nuclear spins, hyperfine coupling creates a fluctuating effective Zeeman field (Overhauser field) felt by electrons, which can be a dominant source of spin qubit decoherence. We characterize the spectral properties of the fluctuating Overhauser field in a GaAs double quantum dot by measuring correlation functions and power spectra of the rate of singlet-triplet mixing of two separated electrons. Away from zero field, spectral weight is concentrated below 10 Hz, with
∼
1
/
f
2
dependence on frequency
f
. This is consistent with a model of nuclear spin diffusion, and indicates that decoherence can be largely suppressed by echo techniques.