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I am wondering what causes a normal shockwave on a wing? I mean why does the airflow (that becomes supersonic over a part of the airfoil) slows down somewhere over that wing suddenly to a subsonic speed (what probably causes a shock).

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The slowdown process occurs at the shock surface. The air entering the shock surface from upstream is supersonic and the air exiting the shock surface downstream is subsonic. The thickness of the shock zone is quite small compared to the chord of the wing.

Sonic shock waves occur because in order for air to get out of the way of something traveling through it, that something has to be moving more slowly than the air's ability to communicate to other parcels of air that "something's on the way". That communication speed is the speed of sound. If the object is moving faster than that, then the air it is running into has no advance warning and cannot start getting out of the way before the object arrives. The result is a shock wave.

The physics of shock waves is well-described on-line.

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