It is the sudden and dramatic rise of wave drag that leads to the concept of a sound barrier.
The von Kármán ogive was a similar shape for bodies with a blunt end, like a missile.
A number of new techniques developed during and just after World War II were able to dramatically reduce the magnitude of wave drag, and by the early 1950s the latest fighter aircraft could reach supersonic speeds.
One common solution to the problem of wave drag was to use a swept wing, which had actually been developed before World War II and used on some German wartime designs.
Sweeping the wing makes it appear thinner and longer in the direction of the airflow, making a conventional teardrop wing shape closer to that of the von Kármán ogive, while still remaining useful at lower speeds where curvature and thickness are important.
This solution was used on a number of designs, beginning with the Bell X-1, the first manned aircraft to fly at the speed of sound.
The downside to this approach is that the wing is so thin it is no longer possible to use it for storage of fuel or landing gear.
Whitcomb had been working on testing various airframe shapes for transonic drag when, after watching a presentation by Adolf Busemann in 1952, he realized that the Sears-Haack body had to apply to the entire aircraft, not just the fuselage.
This meant that the fuselage needed to be made narrower where it joined the wings, so that the cross-section of the entire aircraft matched the Sears-Haack body.
Application of the area rule can also be seen in the use of anti-shock bodies on transonic aircraft, including some jet airliners.
Anti-shock bodies, which are pods along the trailing edges of the wings, serve the same role as the narrow waist fuselage design of other transonic aircraft.
All modern civil airliners use forms of supercritical aerofoil and have substantial supersonic flow over the wing upper surface.