Footsteps? Throat clearing? Singing? Banging a drum and generally acting crazy? Already talking to himself as he walks?
How Polonius hears Hamlet coming can dramatically impact how Hamlet will begin the most famous speech in Shakespeare.
It is a little curious that Hamlet walks in to a place where no one appears to be and then starts talking. Like, is this how it goes down? “Let me go ahead and go to the place the king summoned me to – -Doo de doo de do. – Oh. No one’s here. Well, why don’t I sit myself down and philosophize for a while. That’ll pass the time til whatever’s supposed to happen here happens. . .”
The Hamlet Project 