Soundproofing Deck

I have a duplex that has a top deck and the bottom unit also has an outside lanai (porch) that is right underneath the top deck.

There is little privacy when both tenants are outside on the lanai so I want to soundproof the deck as much as possible. The main concern is the deck is not a solid floor so sound travels in the space between the wood deck.

The deck up top is open - no screening so if it rains and wind is blowing- it could get wet and drip down to the downstairs lanai.

It appears there are two options:

1- put a plywood floor on top of the deck which will cover the holes and then put some type of flooring on top of the plywood-either tile or indoor outdoor carpeting.

2- Put a plywood ceiling on the bottom with some insulation for soundproofing. Because of the possibility of rain coming in the thought was to clear caulk the deck slats so no rain can get drip to the bottom and get into the insulation.

Any thoughts on solving or mitigating this sound problem are appreciated.

Harvey