By critical Mach number you refer to the initial breaking of the sound barrier by an airfoil. As any object moves in air it puts out a bow shock wave. Your motion speeding up the local air. As you approach the speed of sound, called Mach one, you have turbulence develop. As you move faster the air stream reaches a critical point. It implodes behind you as you pass Mach one. The air across the airfoil has reached sonic flow. You don't hear it but the air, the free flowing air stream you just past through reached the speed of sound and then collapsed to its normal pressure. The speed of sound in air is a local thing based on altitude and air temperature.
You could picture pushing a pointed object into a balloon At first it gives and envelops the object. At a certain point the objects pressure will overcome the balloons and it will burst.
The shock wave from a supersonic jet comes a little while after you realize a jet went by.