Gap in ceiling what sould I do?

I built a wall that divided my basement into two different sections. I built in as close as I could to the existing beam/soffet thing as I could. I am now left with a gap a little less then an inch. The gap is two big to stick backer rod into and caulk, so what can I do the seal this gap so sound isn't coming out of it? Any suggestion would be greatly appreciated.

???? I'm confused. Is the gap between two leaves? Or is it bad dry walling?

Some type of perspective would help, like holding your hand or finger up towards the crack to see how big it actually is. But you can twist several lengths of backer rod together and stuff that into the hole or if it is still too large, install a piece of wood or the like to the length of this crack that will allow you to close up the gap to make it small enough to use the backer rod and caulk.

Sorry my picture sucks, the black wall is a new wall that was built, and the gap is between the new wall and an existing beam soffet, thing. The gab is slightly less then an inch big, and there is nothing to rest any caulking on. So installing a piece of wood behind the crack like xspace recomends sounds like the best idea. Any other thoughts?