We use 2.0 Msec of Chandra observations to investigate the cocoon shocks of Cygnus A and some implications for its lobes and jet . Measured shock Mach numbers vary in the range 1.18–1.66 around the cocoon . We estimate a total outburst energy of \simeq 4.7 \times 10 ^ { 60 } erg , with an age of \simeq 2 \times 10 ^ { 7 } yr . The average postshock pressure is found to be 8.6 \pm 0.3 \times 10 ^ { -10 } erg cm ^ { -3 } , which agrees with the average pressure of the thin rim of compressed gas between the radio lobes and shocks , as determined from X-ray spectra . However , average rim pressures are found to be lower in the western lobe than in the eastern lobe by \simeq 20 \% . Pressure estimates for hotspots A and D from synchrotron self-Compton models imply that each jet exerts a ram pressure \gtrsim 3 times its static pressure , consistent with the positions of the hotspots moving about on the cocoon shock over time . A steady , one-dimensional flow model is used to estimate jet properties , finding mildly relativistic flow speeds within the allowed parameter range . Models in which the jet carries a negligible flux of rest mass are consistent with with the observed properties of the jets and hotspots . This favors the jets being light , implying that the kinetic power and momentum flux are carried primarily by the internal energy of the jet plasma rather than by its rest mass .