It may be that you are remembering it was once thought that airplanes could not overcome the speed of sound. There were many stories of airplanes becoming difficult to control due to the excessive vibration and other stability problems that would arise as the sound barrier was approached. This difficulty was more of an engineering problem, rather than an issue arising out of a fundamental physical law, like the theory of relativity. The theory of relativity only applies when velocities approach the speed of light (3x108 m/s), which is nearly 106 times faster than the speed of sound (340 m/s).
When an object passes the speed of sound, there is a shock wave that originates at the front of the airplane and this can significantly affect an airplane if it is not designed to withstand the resulting pressure and drag of the shock waves. The solution was to modify the shape of the airplane and the wings to become more aerodynamical, including narrowing the body and angling the wings further back.
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