  The clumpy stellar wind from the companion star in high mass X-ray binaries
causes variable, partial absorption of the emission from the X-ray source. We
studied XMM-Newton observations from the 7.22 d-long "Cyg X-1 Hard state
Observations of a Complete Binary Orbit in X-rays" (CHOCBOX) monitoring
campaign, in order to constrain the effects of the stellar wind on the
short-timescale X-ray spectral-timing properties of the source. We find these
properties to change significantly in the presence of the wind. In particular,
the longest sampled timescales (corresponding to temporal frequencies of
$\nu\sim$ 0.1-1 Hz) reveal an enhancement of the fractional variability power,
while on the shortest sampled timescales ($\nu\sim$ 1-10 Hz) the variability is
suppressed. In addition, we observe a reduction (by up to a factor of $\sim$
1.8) of the otherwise high coherence between soft and hard band light curves,
as well as of the amplitude of the hard X-ray lags intrinsic to the X-ray
continuum. The observed increase of low frequency variability power can be
explained in terms of variations of the wind column density as a consequence of
motions of the intervening clumps. In this scenario (and assuming a terminal
velocity of $v_{\infty}=2400\ {\rm km\ s^{-1}}$), we obtain an estimate of $l
\sim$ 0.5-1.5 $\times 10^{-4} R_{\ast}$ for the average radial size of a clump.
On the other hand, we suggest the behaviour at high frequencies to be due to
scattering in an optically thicker medium, possibly formed by collision of the
stellar wind with the edge of the disc.
