What can be done about this annoying tree waking me up?

Here is one thing I hate about neighborhoods. The next door neighbor has a huge tree in her side yard; her yard and my side yard are connected. So at certain times of the year a nut or something falls off her tree branch onto my window and wakes me up. If the branches were low I’d cut them back but they’re high up. It sounds crazy but it’s like it’s TIMED to fall just as I doze off to wake me up with a start.
It’s a loud sound as if someone throws a walnut at a window. Is there anything I can put on the window to muffle the sound or something? The screens are up in the attic.