Propeller-driven aircraft cannot break the sound barrier due to aerodynamic limitations inherent in propeller design. The XF-84H Thunderscreech attempted to utilize supersonic propeller blades but was ultimately scrapped due to adverse effects from shockwaves on personnel. Standard propeller aircraft experience flow separation when transitioning from subsonic to supersonic speeds, resulting in a loss of thrust. In contrast, turbojets and turbofans are designed to operate efficiently above the speed of sound.
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Link to wiki article, note the aircraft itself was not super-sonic:rcgldr said:Some aircraft company made a propeller driven plane where the propeller blades operated at super-sonic speed. Although the pilot was shielded from the shock waves, any personel in the general area were adversely affected by the constant bombardment of shockwaves, so they scrapped the program.