Actually I've had this kind of thing from a loose truss rod which resonated on a couple of notes only. Really weird, the whole neck rattles when it goes off!
And as for how I ended up with a truss rod that loose, well my bass has a really solid neck (5 piece neck, sawn in different directions through the grain, its the most stable neck I've ever played) and it never needed more than a tweak on the rod to get the action right

, it just worked its way loose I guess....