We have studied a sample of 28 periodically variable B-type supergiants selected from the HIPPARCOS mission and 12 comparison stars covering the whole B-type spectral range. Our goal is to test if their variability is compatible with opacity-driven non-radial oscillations. We have used the NLTE atmosphere code FASTWIND to derive the atmospheric and wind parameters of the complete sample through line profile fitting. We applied the method to selected H, He and Si line profiles, measured with the

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... high resolution CES spectrograph attached to the ESO CAT telescope in La Silla, Chile. From the location of the stars in the (log Teff, log g) diagram, we suggest that variability of our sample supergiants is indeed due to the gravity modes resulting from the opacity mechanism. We find nine of the comparison stars to be periodically variable as well, and suggest them to be new alpha Cyg variables. We find marginal evidence of a correlation between the amplitude of the photometric variability and the wind density. We investigate the Wind Momentum Luminosity Relation for the whole range of B spectral type supergiants, and find that the later types (> B5) perfectly follow the relation for A supergiants. Additionally, we provide a new spectral type - Teff calibration for B supergiants. Our results imply the possibility to probe internal structure models of massive stars of spectral type B through seismic tuning of gravity modes.