Take a 12 inch prop of reasonable pitch turning at 12K rpm, typical for a decent .60 glow engine (takes about 1.5 bhp). A prop tip is traveling Pi feet each revolution, and at 200 revolutions/sec, the tip speed is Pi X 200 = abt 630 fps. Speed of sound (std conditions - dry air, barometer at sea level, etc) is 1125 ft/sec. Tip speed is nowhere near sonic. Increase the rpm to 21,500 and tip speed will be just up to sonic. That will take about 9 bhp. Got something hotter than nitromethane in that can?
True. the static tip speed is far short of the speed of sound. But you forgot a couple of factors.
1.) The engine will unload in the air and operate at higher rpm. Much higher when the airplane is dove, as gravity provides the horsepower to accelerate the prop.
2.) Tip speed is not simply a function of Pi x D, you have to include the forward travel of the prop with the unloaded tip speed. For high rpm high pitch props, this is significant.
3.) The speed of sound varies with the airfoil moving through the air.