Ping Pong

OK, I've always just accepted that "ping" is onomatopoeia for the sound a bullet makes when it bounces off something... but where does it *really* come from? And where did "pong" come from??? Did "ping" and "pong" enter our language before their use as a nickname for table tennis? And how old an invention *is* table tennis anyhow - and when was it first called "Ping Pong"?