DIY Acoustic Panels

Depends. Thickness, backing, and dimensions determine the absorption pattern. A panel an inch thick on top of MDF won't absorb much below midrange. A panel 2" or more thick with the full empty fire apace behind it will get into the upper bass. Somewhere within that range you can tune by trial and error. Its cheap stuff to play with. Just don't cover with fabric until you know what you want.

I have had a sealed back panel actually resonate.  What happens is the back panel is in contact with the fiberglass/insulation and will resonate with the fiberglass.  I had to cut out a large section of that sealed back to resolve the problem.

@aux/ miller

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.

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.