Virialized Ultra-Light Fields (VULFs) while being viable cold dark matter candidates can also solve the standard model hierarchy problem. Direct searches for VULFs due to their non-particle nature require low-energy precision measurement tools. Here we consider scalar VULF candidates. While the previous proposals have focused on detecting coherent oscillations of the measured signals at the VULF Compton frequencies at the device location, here we point out that VULFs also have a distinct spatial signature, forming dark matter waves. Thereby the discovery reach can be improved by using distributed networks of precision measurement tools. We find the expected dark-matter wave signal by deriving spatio-temporal two-point VULF correlation function. Based on the developed formalism for coherence properties of dark-matter fields, we propose several experiments for dark matter wave detection. In the most basic version, the modifications to already running experiments are minor and only require GPS-assisted time-stamping of data. We also derive the expected dark matter line profile for individual detectors.
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