DIY Acoustic Panels

Open back would absorb energy from Fire Box etc.
That is Higher Freqs finding way to the space behind the panel.

Don't waste your time. It won't do anything either way. The fireplace is most likely not at the early reflection point. Find the early reflection points using the mirror method and dampen these with acoustic tiles. 

I was going to do a 4” thick PVC frame with recycled cotton baffle insulation. Initially thinking that a closed back might be better at least with airflow and sometimes I get water down my chimney when it rains. I ordered some burlap fabric to cover. I do think maybe open back may work to allow some of those low frequencies to pass. I guess like Miller says maybe trial and error. I could always cover later.

Oh I was forgetting being a fireplace of course there's a chimney! Get a copy of Robert Harley's Complete Guide To High End Audio it has a chapter on acoustics and bass traps. Your chimney is in effect a great big port and can be tuned to trap whatever bass frequency you want by simply changing the size and shape of whatever you use across the fireplace and chimney openings.

Its all simple physics relating to the wavelengths of the frequencies you want to tune for. Pretty sure there are tables and description in the book. Been a while, bought it 20-30 years ago. Or you could probably look it up on-line. 

millercarbon, if that is true all you have to do is adjust the damper but it would depend on the length of the chimney. 

Has anyone used "Duck Canvas" for DIY Panels? Is it not transparent enough?