When an object moves faster than the speed of sound it causes a shock wave and consequently a sonic boom. This critical speed is known as Mach 1 and is approximately 740 miles per hour at sea level.
The shock wave from a supersonic aircraft is in the form of two long cones centered on the nose and tail of the aircraft, opening to the rear. For smaller aircraft the shocks are close enough together that they sound like one when they pass, but for larger craft the two remain distinct and cause a "double boom".
As the aircraft increases speed the cones grow "tighter" around the craft, and do not become much "louder". At very high speeds and altitudes the cone does not intersect the ground, and no boom will be heard. The power, or volume of the shock wave is dependant on the amount of air that is being sped up, and thus the size of the aircraft.
Sonic booms generate enormous amounts of sound energy. Typically the shock front may approach 100,000,000 watts per square meter, and may exceed 200 decibels.
Fighter jet pilots easily notice the difficulty and air resistance in approaching the speed of sound, and also the ease and rush of forward acceleration instantly after passing mach 1.
The first human to go supersonic was General Chuck Yeager U.S.A.F. on OCT.14 1947, after a long string of around 500 test pilot fatalities in the attempt!
Most commercial jets fly at 0.87 Mach. Although that is the jet speed, the air speed around the wings is around 0.98 Mach, and can sometimes cause handling problems at 0.99 Mach. It is called "Mach buffet" and pilots hate and fear it.
In the late 1950s when SST designs were being actively pursued it was thought that although the boom would be very large, they could avoid problems by flying higher. This premise was proven false when the North American B-70 Valkyrie started flying and it was found that the boom was a very real problem even at 70,000ft (21,000m). This eventually doomed most SST projects.
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