The transonic flight regime can be one of the most difficult for aircraft. Drag goes up nearly exponentially as you approach Mach 1, which is why it’s expensive to fly at or just below the speed of sound; in principle, it can be more fuel efficient to fly *faster* than sound. And some low-supersonic transport designed were studied back int he 70’s and thereabouts, designed to move at up to about Mach 1.4 But as with every Really Cool Thing, the additional costs and complexities (including sonic booms rattling the suburbs below) ended up trashing the idea of slightly-supersonic transports.
The interesting thing is… a distinctly subsonic aircraft can move, at least in part, faster than the speed of sound relative to the air going by it. An airplane with an air speed of, say, Mach 0.8 needs to shove air out of the way. Air needs to flow around fuselages, wings and engine nacelles; by flying around these structures, the air – relative tot he structure – has to speed up… and then slow down again as the structure tapers off. This can often mean that air is flowing at or even beyond the speed of sound in localized regions. if you know what to look for, and if the lighting conditions are just right, you can actually make out the standing shock waves from airflow that has been shoved past Mach 1.
“Real world” shockwaves are difficult to see. They can be seen far more clearly in wind tunnels where the lighting can be carefully controlled.