Dry, worn metal-on-metal contact at a hinge pin locks under static friction while the door's motion elastically winds up torque at that contact — like an invisible torsion spring. Once the torque exceeds the static friction limit, the contact suddenly slips under the lower kinetic friction, then relocks almost immediately. Each release pumps a pulse of energy into the hinge bracket, which rings briefly at its own damped resonant frequency:
f = (1 / 2π) · √(k / I)
k is the hinge's structural stiffness, I the effective inertia of the swinging door — heavier doors creak lower, stiffer hinges creak higher. Rust widens the static/kinetic friction gap (louder, sharper creaks and visible flaking); lubrication shrinks that gap until the stick-slip cycle — and the sound — disappears.