Well,
we call FAN, not only the fanatics, but also the first set of spinning blades on the 2-way jet engines, this is the first black bladed wheel with thte nosecone of the engine what you see when you are in front of the engine. Fan is exactly a very very dense propeller, that is spinned by the jet engine behind it.
This fan produces an unbeliavable amount of thrust compared with the "regular" jet engine behind it. Therefore it is a key part of the engine: it produces the most thrust, it produces a slow flow around the engine which reduces its noise, and it saves the intake of the jet part from birds too.
I think designers does not make supersonic fans, because the blade shape would be too difficult, and maybe they would not get as many thrust from it as in subsonic speed. Also, the speed is increasing as you go farther on the blade edge. This means the airflow speed is not constant at each diameter, and it can be supersonic at outer diameters, but sub-sonic in smaller diameters. To make such a blade which have supersonic flow on its whole length requires a very rigid material which we no have currently. It is still amazing to see a GE90 engine with its 310 cm diameter fan !!! Incredible. Almost the size of the 737 fuselage.
And another small info. Do you know how much is the speed at the outer diameter of a car turbocharger wheel
It can exceed M3.0 !!! Now, if you see that small wheel, with its relatively fat blades, it is easy to imagine this spinner in 3 metres size ! An engine that could spin it would be a fueleater, and I think it would not produced much thrust...
The soundspeed is somewhere 1230 km/h... it depends on temperature and pressure of course. For example the RR Trent 900 engines of Airbus A380 have a nearly 3m diameter fan with 3500rpm fan speed, which is nearly 550 m/s = 2000 km/h = M1.6 at blade end.
Look at that size...
http://upload.wikimedia.org/wikipedia/commons/thumb/0/07/Ge-747-N747GE-020918-03.jpg/800px-Ge-747-N747GE-020918-03.jpg
