I think most of us enjoy the visuals associated with shock waves. These things have made the rounds on teh innertoobs (Google Image and YouTube, et al). The hip, media-savvy teachers use them when teaching waves.
The deep explanation is, well, robust.
Check out the new pic:
A U.S. Air Force F-22 Raptor aircraft participating in Northern Edge 2009 executes a supersonic flyby over the flight deck of the aircraft carrier USS John C. Stennis (CVN 74) while the ship is underway in the Gulf of Alaska on June 22, 2009. The visual effect is created by moisture trapped between crests in a sound wave at or near the moment a jet goes supersonic. Credit: DoD/Petty Officer 1st Class Ronald Dejarnett, U.S. Navy
"The Prandtl-Glauert Singularity"? Sounds like the title of an episode of The Big Bang Theory.