My husband and sons built a wooden wall in our backyard to use as a ball wall for soccer and lacrosse. Our boys bounce the ball off the wall to practice. It is about 10X10 frame with plywood affixed on it. It stands about 2 feet from our home which has siding on it. When they practice the sound reverberates throughout our neighborhood. I would like to stay on the good side of our neighbors. How can we cut the noise of the ball hitting the wood down?
You could put a few layers of cement board on the back side of the plywood.
I would use two layers of 1/2 inch cement backer board and use outdoor grade construction adhesive in conjunction with screws.
Start with one layer and see how it sounds.
There will be noise from the wall reverberating and there is noise from the ball bouncing against it. The only way to not have wall reverb is to make it more solid, i.e. concrete or maybe an extreme number of layers of plywood. But you will still have the ball noise. There is a concrete wall in my neighborhood that kids use for handball and tennis practice. It's 500 yards away from me but I can still hear those balls slapping it. If it were me, I wouldn't worry about it until someone complains and just embrace it as the sounds of youth. Your sons will grow up and leave some day and you will miss those sounds...