How did the sound barrier change the shape of planes?

Slow-flying planes were never affected by air waves. As planes began to fly higher and faster, some pilots found that they encountered difficulties — the planes vibrated fiercely and the pilots couldn't operate the controls. What these pilots encountered was wave drag; that is, the piling-up of air in front of the plane — the sound barrier. Scientists and airmen studied this effect on planes and soon recognized what was happening.
To honor the man who first explored this subject scientifically, we measure the speed of a plane or rocket in Mach numbers. Aeronautical engineers use Mach 1 as equal to 680 miles per hour, the speed of sound at about 35,000 feet and higher, where the temperature is 50 °F or lower. Mach 2 equals twice the speed of sound or 1,360 miles per hour.
They found that the shock waves which caused wave drag were shaped like a cone. If the plane has long wings, it tends to spin more easily. As a result, jet planes, designed to fly faster than sound, have shorter wings set farther back along the sides of the body