This question is inconsistent, because it assumes that a world which doesn't produce sounds that are not heard would have trees that fall outside of perception. Perhaps the tree is seen from a distance? In any case, the intended question is really "Does the physical universe exist outside of our perceptions?"
The world we perceive (the phenomenal world) is fully and consistently conceptualizeable in physical terms. If the nature of the universe is in fact not physical (so that the falling tree does not make a sound), this fact is epistemically inaccessible. However, the fact that the universe acts consistently enough that our theories of its operation are consistently corroborated makes them useful concepts even if they are, objectively speaking, false. They may or may not be objectively correct, but they are intersubjectively correct*.
Theories which produce accurate predictions can become conceptual frameworks . If we refer to a 'sound wave' as a real thing, that is a valid concept even if there is no 'real' air to be vibrating: our concept merely refers to a different underlying noumenon than we imagine. Our constructed world is consistent, and has a place for sound; so long as the universe continues to supply us with phenomena which support these constructions, sound is a valid concept.
If we wish to make the application of these constructions completely valid, we must make our claims in terms of perceptions (that way they can be tested). Well, we are assuming we don't hear the sound of the tree - and sound is transient. But it could have effects, knocking dust around in a particular way or something recognizable. This would be indirect, yes. But if we saw the wave on an oscilloscope would we have really seen any more? What about hearing the sound directly? In all three cases have perceived that something affected the environment in a way which we characterize as 'sound'. Whether the universe actually had vibrating waves or filled in the details as we looked for them, the end effect upon us is the same. We could choose to call all of these effects sound.
Essentially, we have information about what the noumenon can be, because whatever it is, is must be something which is capable of producing our perceptions. Any noumenon which could not cause our perceptions must be rejected. We are not a simulation run on a two-state Turing machine with a four-bit-long tape, because at any given moment we perceive more information than that entire system contains.
*Before everyone jumps on my assertion that our scientific theories are correct: I am referring to the basic understandings we have about matter: things have extension, weight, make sounds upon collision. Especially that one, considering the matter at hand. If you wish to debate that these provide accurate predictions...
Converse56, there is a collossal difference between
"Our patterns of perceptions ... are so very much like the world which we have constructed and called 'physical reality' that our intuitions and theories concerning our construction bear much explanatory and predictive power over our perceptions, and thus the universe."
"The world we perceive is so much like the world we perceive, that the world we perceive is like the real world."
The former states that we have some information about the noumenon by way of our models (not our direct perceptions, as you seem to indicate), because the phenomenon is contained within the noumenon. The latter, your farcical repeat, states that the noumenon is contained within the phenomenon, a (probably unintentional) straw man you proceed to demolish quite effectively. Congratulations, you just said '1+1 != 732', and then said that 'my brand of logic' claimed the contrary.