The second stage of Apollo 11 generated a greater than 20 deg shock-wave half angle which corresponds to less than $1000 \frac{m}{s}$ forward speed not 6000 mph ($2682.24 \frac{m}{s}$)?
I measured the half angle of the shock-wave generated by the second stage of Apollo 11 after separation (see the picture). This angle is greater than 20 deg.
Using the relation that gives the velocity of an object as a function of the speed of sound and the half angle of the shock-wave, I got:
${{V}_{Stage\ 2}}<\frac{1225\frac{km}{h}}{\sin \left( 20{}^\circ \right)}=994.90\frac{m}{s}$
According to NASA, at burnout, the first stage had 6000 mph.
In appears that, after separation, stage II advanced only at 994.9 m/s / 6000 mph = 37.09% of the stated speed (6000 mph). How is it possible?
Source: Video, First Stage Separation, Apollo 11
A more clear picture of the same event.
Source: Saturn V
Update
Another picture, from the same video, shows the shock-wave created by the leading edge of Saturn V. It is visible due to the cloud of gas formed around the entire rocket when the first stage retrorockets fired during separation. The same half angle, greater than 20 degree, appears.