The Sonic Boom, as seen above, is caused by the Doppler Effect - that thing Sheldon explained on the Big Bang Theory.
When an object is stationary, while emitting sound, the sound waves spread out uniformly in a circle from the source, as seen in the second image, however when that object begins, as seen in the third image, to move the circles are not emanating from the same position, so the troughs and crests (represented by the black lines) of each wave are in are closer together on one side and further apart on the other.
So when the object is traveling at the speed of sound all the troughs/crests are perfectly aligned on one side, where they then amplify each other (positive and negative superposition) producing a loud burst of sound and also pressurising the air close to the source which is why a cloud is seen.
This effect can also be observed with light, theoritically, however first we need to make something that can, somehow, reach the speed of light ;)
We have to design high speed rail tunnels so that there are no residual effects from air vibrations caused by trains passing through a tunnel. The criteria ensures passenger comfort is maintained. When the first shinkansen were built in Japan, unforeseen aerodynamic effects caused passengers to feel discomfort as they passed through tunnels; since then, design has advanced and the aerodynamic effects are mitigated, usually by inclusion of ‘porous’ portals at the entrance/exit to the tunnel which allow the pressure waves to dissipate.