Hi Basketball,
When the pilot wants to increase the RPM they move the prop lever forward in the cockpit. This then adjusts the tension on the speeder spring. The governor now wants equilibrium at a higher RPM. The old RPM is now considered to be an underspeed condition and the governor corrects accordingly.
The new tension in the speeder spring fights against the forces generated by the spinning fly weights at the old RPM. This new speeder spring tension wins out and moves the pilot valve into a position which lets more oil into the hub, forcing the blades to finer pitch. This results in less prop torque and the RPM increases.
Another case is if the pilot does not change the position of the prop lever but the RPM starts to increase because, for example, the pilot has started a descent. In this case the flyweights spin faster and overwhelm the tension of the speeder spring. The pilot valve then moves into position to allow oil to drain out of the hub and back into the sump. The drop in pressure in the hub allows the blade angle to coarsen and the increasing prop torque works against the increasing RPM.
If we increase RPM and then power with a CSU this is what happens:
Step 1) Prop lever set for higher RPM - blade angle decreases to allow for the higher RPM.
Step 2) Power increased - the added engine torque now starts to overwhelm the prop torque generated with the finer pitch so the governor coarsens the blade angle again to compensate.
The eventual TAS you get will depend on the thrust/torque ratio you are getting out of the prop for the RPM airspeed combination you have.
You normally apply finer pitch for take-off, when climbing and as a precaution just before landing. The thrust/torque ratio is closer to optimal with finer blade angles when operating at lower speeds e.g. take-off, climb, landing (in case of go-around).
If you were in cruise at the manufacturer's recommended cruise settings and you applied fine pitch you would get a drop in TAS. This is because at cruise speeds the finer pitch and higher RPM means the prop is no longer working as efficiently as it was before and thrust drops away.
Cheers,
Rich