Diagnose a noise by what it sounds like - a clunk, a whine, a tick, and a squeal each point at a different system.
Clunk:
- Over bumps - worn sway bar end links (the most common Miata clunk), tired shocks, or subframe bushings.
- On gear engagement or throttle on-off - driveline lash: worn differential bushings, driveshaft U-joints, or clutch.
Whine:
- Rises with road speed, changes when you load the car in a turn - a wheel bearing.
- Rises with road speed, steady - the differential.
- Rises with engine rpm - an accessory: alternator, or power steering if equipped.
Tick:
- From the top of the engine - valve lash on an NA or early NB, or a lifter. A light injector tick is normal.
- From the front timing cover on an NC/ND - chain guides or tensioner.
Squeal:
- On cold start or with accessories - a glazed or loose accessory belt.
- When braking - the pad wear indicator or glazed pads.
To pin it down: note whether the noise follows rpm or road speed, whether it changes when cornering (loads bearings), and whether it appears hot or cold. Those three questions eliminate most of the list before you touch a tool.