During World War II, the current United States Air Force (USAF) was then known as the U.S. Army Air Force or USAAF (the popularized "Army Air Corps" was the former name from 1926-1941). Flyers were considered a department of the Army until 18 September 1947, when all air activities were transferred to the new Air Force. Chuck Yeager flew into history less than a month later on 14 October in the cockpit of Glamorous Glennis. The smashing of the sound barrier can be considered a small part of the Air Force's first project, which was to investigate methods of improving aircraft performance at high Mach numbers and speeds.
The 1983 movie hit The Right Stuff does a great job chronicling the chase for the "World's Fastest Man," and it starts by showing Yeager's achievements in the pursuit of the sound barrier. On the night of 13 October 1947, Yeager did in fact break two ribs while riding his horse near the newly-christened Edwards Air Force Base (formerly known as Muroc Army Air Base). He flew in that condition the next morning on Glamorous Glennis (named in honor of his wife) when he broke the sound barrier. Yeager experienced some instability in the charge up to Mach 1 (this unstable region of speed is known as the "transonic" area) but successfully piloted the craft through the sound barrier and shook the desert landscape with the deafening sonic boom that Edwards AFB would be famous for from that point on. The "transonic" instability that Yeager experienced was a result of the laws of aerodynamics: when a vehicle approaches Mach 1, some of the air flowing around that craft is already moving faster than the speed of sound. This can create inconsistencies in the regular handling of an aircraft that make it "hectic," as Yeager put it. A video below highlight's Chuck Yeager's immortalized 1947 flight.
The Bell X-1 that Yeager broke the sound record in was remarkably similar in shape and design to one of the previous speed record holders: the Me-163 Komet of the World War II German Luftwaffe. The German craft was intended as a miracle air weapon that would save Germany from the relentless heavy bombing campaign of the later years, but it was ironically so fast that it could not effectively engage Allied bombers. The Bell X-1, however, had four liquid oxygen rocket motors that could be fired individually. Also, in a concept that would be repeated throughout the Air Force's X-Program and mimicked for decades afterward, the X-1 vehicle was carried up to a high altitude of 20,000 feet or more and then dropped from its B-29 Superfortress bomber carrier aircraft. Future test vehicles utilized in this manner would use the B-52 Stratofortress platform, a bomber that is still in operation today. Interestingly, Yeager actually performed a conventional take off with an X-1 in 1949. Like its predecessor the Komet, the X-1 climbed like a demon; Yeager made it up to 23,000 feet in less than 90 seconds.
Many flight engineers of Chuck Yeager's day believed that the sound barrier could not be broken. They thought that it was an absolute idea that humans were not meant to surpass. Yeager did not share this theory, and so was quite willing to test the concept. The Bell X-1 Yeager flew was the first in a long series of aircraft like the X-2, X-3, and X-15 designed to push the "outside of the envelope" and test new ideas of aircraft engineering. Its distinctive orange color streaking through the sky is representative of the bravery of the military and civilian test pilots that flew the X-1 and craft similar to it. It is pictured below in the Smithsonian Air and Space Museum next to other history-making craft such as the Spirit of St. Louis and SpaceShipOne (Burt Rutan's civilian spaceship that set altitude flight records), a craft that looks oddly similar to the X-1 despite its vastly different purpose.

SOURCES
http://commons.wikimedia.org/wiki/File:Chuck_Yeager_with_GlamorousGlennis.jpg
http://www.youtube.com/watch?v=dke2i-xO1uo
http://commons.wikimedia.org/wiki/File:Bell_X-1_color.jpg
http://www.members.tripod.com/derekhorne/yeagerx1.html
http://commons.wikimedia.org/wiki/File:Ss1_smithsonian.jpg