Did you know…
What happens when a plane goes supersonic?
Short answer
When an aircraft passes Mach 1 the air can no longer move out of its way in advance, so pressure disturbances pile up into shock waves at the nose, wings and tail. Drag jumps sharply, the centre of lift shifts aft, controls change feel, and those shock waves trail behind as a continuous sonic boom heard along the whole ground track.

Air that cannot get out of the way
Sound is a pressure wave, and at subsonic speeds the air ahead of an aircraft receives advance warning through those waves: the flow begins to divert around the nose and wings before they arrive. At Mach 1 the aircraft is travelling as fast as the warning, and the disturbances can no longer propagate forward. They pile up into extremely thin regions where pressure, temperature and density jump almost discontinuously. These are shock waves, and every supersonic aircraft carries a set of them attached to its nose, canopy, wing leading edges, inlets and tail.
The transonic transition
The uncomfortable part is not being supersonic but getting there. Air accelerates as it curves over a wing, so parts of the flow reach Mach 1 while the aircraft is still at Mach 0.8 or so. Local shock waves form on the upper surface, the boundary layer behind them separates, and drag rises steeply. On the early aircraft that probed this region the effects were dramatic: buffeting, a nose-down pitching tendency called Mach tuck, ailerons that reversed their effect, and elevators frozen by the shock wave sitting on the tailplane. The Bell X-1 solved the last of these with an all-moving horizontal tail, and the design tools that followed, swept wings, thin sections and area ruling, allowed later aircraft to pass through the region smoothly.
Life on the far side
Once fully supersonic the flow becomes more orderly. The shocks stabilise, drag settles at a higher but predictable level, and the aircraft flies with the centre of lift moved rearward, which on Concorde was compensated by pumping fuel aft into a trim tank. The air compressed through the shocks also heats up: at Mach 2 the nose of Concorde reached about 127 °C, and the airframe stretched by around 25 cm in cruise. Engine inlets need movable ramps or spikes to slow the incoming air to subsonic speed before it reaches the compressor. The pilots feel little; the Mach meter is the only clear sign that anything has changed.
The boom that follows
The shock waves do not stay with the aircraft. They spread outward in a cone and reach the ground as a sudden pressure rise followed by a drop, heard as a double bang. The boom is continuous along the entire supersonic track, which is why overland supersonic flight has been banned in most countries since the 1970s and why NASA's X-59 is testing a shape that softens the signature.
More questions

Physics of flight
Why can't a Corsair pilot apply full power when going around after a failed carrier landing?
Because at low speed and high power the Corsair would drop its left wing suddenly and with almost no warning, due to propeller torque. If the throttle was… more…

Physics of flight
What did the phrase "banking with intent to turn" mean among F-104 pilots?
It was a joke among Canadian F-104 pilots: banking the aircraft "with intent to turn" referred to its poor low-speed turning. Its sustained turn capability… more…

Julian Herzog (Website) (CC BY), vía commons Physics of flight
What is "flight envelope protection," which the A320 pioneered?
A set of limits embedded in the flight control software: it calculates the flight envelope, adds a safety margin, and blocks pilot inputs that would take the… more…

Julian Herzog (Website) (CC BY), vía commons Physics of flight
What is the A320's SHARP package for?
SHARP (SHort AiRfield Package) improves takeoff and landing performance on short runways and is designed to increase low-speed lift. It combines aerodynamic… more…

Physics of flight
What flaw sank Vought's all-metal V-141 fighter?
It wasn't a single flaw: tests showed the V-141 still flew poorly, was prone to spinning, and also suffered tail flutter, which is why it was rejected. It… more…

Physics of flight
What wind tunnel did NACA use to study the Corsair, and how big was it?
The full-scale 30- by 60-Foot Tunnel at the Langley Research Center, in Hampton, Virginia. NACA dedicated the facility on 27 May 1931 and used it to test the… more…