I am doing a renovation of a room on a second floor. I removed the old parquet floor, which was glued on a 5/8 inch t/g plywood. I removed the squeaky floor sounds by adding more screws into the joists. I then decided to soundproof the floor by adding an acoustical membrane 9 mm. thick. Over this membrane I installed a 3/4 inch plywood T/G, with the non T/G edges glued together. I left a 1/4 inch gap around the perimeter of the room. I want to nail or staple 5 1/4 inch wide solid maple wood floor planks over this plywood, (not engineered floor). I was told not to screw down the plywood, but it is bouncy, when someone walks over the plywood you can see the plywood bounce up and down. Now I am stuck, I cannot solidify the plywood with nails or screws because it will cancel the soundproofing of the membrane. My question: If I don't screw down the plywood, will the weight and the nails of the hardwood solidify my floor and stop the bouncing or will the whole floor bounce up and down and eventually break or crack my floor?
Just to clarify, the membrane is sandwiched between the first plywood and the second plywood.
I would be very appreciative of getting advice from a professional. Thanks

I think that your new flooring would hold the plywood down. You could make an experiment by laying bundles of the new flooring in place over the plywood without opening up the bundles that should cover the floor and see if it lays down securely. Nailing it into place would help keep the plywood in a plane and add lots of weight.

Thanks for your reply Pete A., I will lay down the hardwood as you mentioned and see if the weight of the planks will solidify the plywood.

Yes the weight plus the fasteners holding it together will keep it flat. I've done a few floating subfloors.