Well, seeing as the riddle is meant to poke fun at us and make us think, let's poke fun at the riddle.
Let's go ahead and assume that existence is based on perception, and that said tree that falls in the woods with no observers around makes no sound, because there is no one to hear. Why stop there? Unless someone is deaf, they probably couldn't be close enough to see, smell, touch, or taste the tree if they can't hear it falling. Since this tree thus can't be perceived by any means, it's safe to conclude, based on our earlier assumptions, that the tree, having no perceivable properties, simply does not exist. Problem being, the statement is still a conditional. If a tree is falling in the woods and no one is there to hear it, does it make a sound? The two conditions are that the tree falls (to fall, it probably has to exist first) and that no one can be around to hear it (and logically, with few exceptions, also see, smell, etc.= perceive it). So if this tree, with no one around to perceive it, can somehow struggle on, exist, and even fall (little trooper), then I think it's fair enough to say that it would also retain its properties of sound.
So with this line of thinking, the answer is yes, the tree does make a sound. Or, if you're a cynic and wish to add all those exceptions and possibilities, like a deaf person who can't hear the tree but can otherwise perceive it, then at worst the answer is sometimes. In conclusion, if you've stuck with this entire thing, you either really like philosophy or you're really bored. In either case, this post came from my own boredom and one of those ideas that seemed really cool because I was so bored. It may be much less interesting (or accurate) than I first thought. At any rate, it's an interesting idea to propose to your philo professor.
