We build a full spectral-timing model for the low/hard state of black hole binaries assuming that the spectrum of the X-ray hot flow can be produced by two Comptonisation zones. Slow fluctuations generated at the largest radii/softest spectral region of the flow propagate down to modulate the faster fluctuations produced in the spectrally harder region close to the black hole. The observed spectrum and variability are produced by summing over all regions in the flow, including its emission reflected from the truncated disc. This produces energy-dependent Fourier lags qualitatively similar to those in the data. Given a viscous frequency prescription, the model predicts Fourier power spectral densities and lags for any energy bands. We apply this model to archival RXTE data from Cyg X-1, using the time-averaged energy spectrum together with an assumed emissivity to set the radial bounds of the soft and hard Comptonisation regions. We find that the power spectra cannot be described by any smooth model of generating fluctuations, instead requiring that there are specific radii in the flow where noise is preferentially produced. We also find fluctuation damping between spectrally distinct regions is required to prevent all the variability power generated at large radii being propagated into the inner regions. Even with these additions, we can fit either the power spectra at each energy, or the lags between energy bands, but not both. We conclude that either the spectra are more complex than two zone models, or that other processes are important in forming the variability.

15 pages, 12 figures, Published in MNRAS