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.
A friend of mine who is former fighter pilot and trainer for the Navy wants me to point out that these clouds are not formed it the moment someone breaks through the sound barrier. They are often formed before and they continue as long as the plane is flying through sufficiently moist air at near the speed of sound. They often look like planes flying with tutus. M.S. Cramer, Engineering Science and Mechanics Professor at Virgina Tech, describes how these come about for his fluid mechanics text
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Its not always that coned shaped clouds are shock waves. these are pressure waves caused by the difference in pressure. These often occur before the plane.
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