The double dings being described are caused when the shaft hits the edge of something while the cue was either not being held, was being held with a very light grip, or was being held only near the butt. The shaft flex (think diving board) causes it to rebound off the object slightly and hit it again a split second later. The shaft vibration and flex absorbs or disepates most of the energy so that there is usually only one bounce good enough to cause an additional ding. The second ding is slightly off from the first because if the cue is being held, it was usually in some kind of forward or backwards motion at the time of contact with the object edge. It it was dropped it was usually in downward motion at contact. If the butt was against the floor it may kick out slightly after the first impact which causes the second ding to be slightly off from the first. The most common double ding culprits:
1) The cue hits the edge of a table, chair, pool table, etc (most common cause). This usually happens when you go to lean the cue against the table edge (or are picking it up) and drop it, when you are holding or carrying the cue upright with the butt on or near the floor and lose your grip causing the cue to fall over and hit the edge of something.
2) Leaning your cue up against a table edge and letting it fall down the last couple of inches instead of making sure the cue is fully against the table before letting it go. You often see players half throw/lean their cue down against the table edge in disgust after their turn at the table is over.
3) The sometimes sharp rail edge where it meets the rail rubber on some tables can also can these double dings when the shaft hits it. This can happen when you hit or tap the rail with the cue in anger after a missed shot, to remove excess chalk, and even when you occasionally lose your grip on the cue while addressing or getting down on a shot and the shaft falls onto the rail or corner piece. Also, lowering the shaft onto the rail too hard when using the cue to judge bank or kick angles.
Kevin