Black hole low-mass X-ray binaries show a variety of variability features, which manifest themselves as narrow peak-like structures superposed on broad noise components in power density spectra in the hard X-ray emission. In this work we study variability properties of the band-limited noise component during the low-hard state for a sample of black hole X-ray binaries. We investigate the characteristic frequency and amplitude of the band-limited noise component and study covariance spectra. For observations that show a noise component with a characteristic frequency above one Hz in the hard energy band (4 - 8 keV) we found this very same component at a lower frequency in the soft band (1 - 2 keV). This difference in characteristic frequency is an indication that while both the soft and the hard band photons contribute to the same band-limited noise component, which likely represents the modulation of the mass accretion rate, the soft photons origin actually further away from the black hole than the hard photons. Thus the soft photons are characterized by larger radii, lower frequencies and softer energies, and are probably associated with a smaller optical depth for Comptonisation up-scattering from the outer layer of the corona, or suggesting of a temperature gradient of the corona. We interpret this energy dependence within the picture of energy-dependent power density states as a hint that the contribution of the up-scattered photons originating in the outskirts of the Comptonising corona to the overall emission in the soft band is becoming significant.