  Multifrequency observations from the VLA, VLBA and OVRO Millimeter Array of a
major radio outburst of Cygnus X-3 in 2001 September are presented, measuring
the evolution of the spectrum of the source over three decades in frequency,
over a period of six days. Following the peak of the flare, as the intensity
declines the high-frequency spectrum at frequency nu steepens from nu^{-0.4} to
nu^{-0.6}, after which the spectral index remains at this latter terminal
value; a trend previously observed but hitherto not satisfactorily explained.
VLBA observations, for the first time, track over several days the expansion of
a sequence of knots whose initial diameters are approximately 8
milliarcseconds. The light-crossing time within these plasmons is of the same
order as the time-scale over which the spectrum is observed to evolve. We
contend that properly accounting for light-travel time effects in and between
plasmons which are initially optically thick, but which after expansion become
optically thin, explains the key features of the spectral evolution, for
example the observed timescale. Using the VLBA images, we have directly
measured for the first time the proper motions of individual knots, analysis of
which shows a two-sided jet whose axis is precessing. The best-fit jet speed is
roughly beta = 0.63 and the precession period is about 5 days, significantly
lower than fitted for a previous flare. Extrapolation of the positions of the
knots measured by the VLBA back to zero-separation shows this to occur
approximately 2.5 days after the detection of the rise in flux density of
Cygnus X-3.
