So, pardon my ignorance but, fan, compressor and turbine blades reach supersonic speeds commonly?
I thought that was undesirable.
It generally is, but since the speed is greatest at the tip of the blade therefore any part of a blade on the same rotor that is smaller than the fan tip diameter will not be supersonic. A little bit of trading going on for a short period of time just to keep the turbine happy, then along comes geared fans and a win win