A door hinge doesn't creak because it's "old" — it creaks because dry metal-on-metal contact at the pin exhibits stick-slip friction. As the door swings, the microscopic asperities of the pin and knuckle stay locked (static friction) while the door's motion elastically winds up torque at the contact, like a tiny torsion spring. Once that torque exceeds the static friction limit, the contact suddenly releases and slides under the lower kinetic friction — then relocks almost immediately, and the cycle repeats many times per second.
Each release dumps a small pulse of energy into the hinge bracket, which rings at its own damped resonant frequency:
f = (1 / 2π) · √(k / I)
where k is the hinge's structural stiffness and I is the effective inertia of the door being swung (bigger, heavier doors creak lower; stiffer hinges creak higher). Rust and dryness raise the gap between static and kinetic friction, making each release stronger — louder, sharper creaks. Lubrication shrinks that gap until the stick-slip cycle stops altogether, which is exactly why oiling a hinge silences it.