Swept back wing theory
Imagine a wing that is infinitely long, and stretches from east to west. It is moving north at 400 mph. Obiously, it does not produce a shockwave, as it is moving subsonically.
Now, imagine a copy of this wing  that is moving to the east at 800 mph (along its length) while still moving north at 400 mph. Other than skin effects, this wing is aerodynamically identical to the first, so it does not have shockwaves, yet it is very supersonic.
Of course, a real swept wing is not infintely long, and so there are shockwaves at nose and tip of the wing, but mid span it really does behave similarly to a wing moving much more slowly perpendicular to its leading edge.