We reported previously that for Cyg X-1 there is a settling period following the transition from hard to soft state (astro-ph/9610071). During the transiton, The low energy spectrum (below ~10 keV) varies significantly from observation to observation while the high energy portion changes little. The source reaches nominal soft-state brightness during the settling period. It can be characterized by a soft low-energy spectrum and significant low-frequency 1/f noise and white noise on the power density spectrum (PDS). The low-energy spectrum becomes even softer, and the PDS is completely dominated by the 1/f noise, when the ``true soft state is reached. In this paper, subsequent RXTE observations of Cyg X-1 in the soft state are examined, and the results confirm our earlier conclusions. Furthermore, we show the results from observations taken during a soft-to-hard transition. As expected, the white noise appears again, and accordingly, the 1/f noise becomes less dominant, similar to the settling period at the end of the hard-to-soft transition. The low-frequency 1/f noise has not been observed when Cyg X-1 is in the hard state. Therefore, it seems to be positively correlated with the disk mass accretion rate which is low in the hard state and high in the soft state. The difference in the observed spectral and timing properties between the hard and soft states is qualitatively consistent with a simple ``fluctuating corona model (astro-ph/9610071). Here we present more evidence for it.
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