  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.
