Diagnosis
That loud hum is usually the cooling fan motor starting to fail. Its bearings wear out or it gets off-balance. It's located behind the vent grille on top of the unit.
How to Fix It
Unplug the microwave. Remove the filters and the vent cover. You'll see the fan mounted. Check for any obvious debris jamming the blades. If it's clear, the motor itself is likely the issue. Disconnect its wiring, remove the mounting screws, and replace the entire fan motor assembly. It's often easier to replace the whole unit than try to repair the motor.
If That Didn't Work
A less common but similar noise can come from the turntable motor. If the noise changes when you remove the glass tray and roller ring, that's your culprit. The fix is the same process: unplug, access, and replace the motor.
Heads Up
When ordering a replacement fan motor, you need the exact part for the R-1874T. Motors from other Sharp models might look similar but have different RPMs or mounting points. The model number is on a sticker inside the door or on the side of the cabinet.