The noise power spectra of the fluctuations in density of a vibrated column of granular material are found to be time dependent. Spectral analysis of these noise power fluctuations shows nontrivial frequency dependences. The noise powers at different frequencies are also found to fluctuate in a partially correlated way. In most instances, the slow variations of the noise are strongly correlated over a broad range of frequencies. These results indicate that highly cooperative interactions exist between fluctuators. In contrast, effects of such strongly coupled fluctuators are absent in the one-dimensional parking-lot-model, one of the simplest systems used to provide a model for recent granular compaction experiments.