My Mazda MX-5 is making a weird, constant droning noise. It kind of sounds like there is a prop-airplane flying above it or a motorcycle about 20m away. It begins to get audible above 40kmh, but does not vary with engine speed and persists even when I disengage the clutch and coast. Could it be caused by a worn belt somewhere?
The sound you describe is typically caused by a "rolling defect" arising from tyres or wheel hubs. Since it persists even while coasting with the engine at idling speed, you can eliminate any of the moving components of the engine.
It is not uncommon for a single tyre to develop a fault which can create a droning noise. Such a problem is not always detectable by visual inspection.
While it may not always be convenient, the best way to check is to swop a set of four wheels and tyres. However, if your tyres are near the end of their useful life, just replace all four.
This exercise may not be necessary if your workshop can raise the car on a chassis and spin the wheels. If there is a humming or even faint rumbling noise, the wheel bearing is worn.
Replacing the defective bearing will be the only solution, as it is not a component which can be repaired. It is recommended that the bearing sets on all four hubs are replaced at the same time. This is neither overly difficult nor complicated and, in most cars, all four sets can be replaced in under four hours.