I read that the heavier the material the better it blocks sound.
Then why do people stuff their walls with soft insulation like mineral wool.
Why not just put clay/ceramic tiles or wooden boards If the purpose is to decrease decibel levels ?
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This is difficult to answer, because we can't read people's minds, but assuming it is correct that, for example, tile would cut the sound better than mineral wool, there are a lot of practical barriers:
Tile is not made for this, it would be very difficult / impossible to install. Bat insulation can just be stuffed in between studs and it stays in place while the wall is being sheathed on its own. Tile would keep falling out.
Tile would be much more expensive. For example, in my area, a roll of R11 insulation for a 2x4 wall cavity is about $10. This covers 50 sq ft, or 14.6 cu ft. The cheapest ceramic tile I can find here is $1.59 sq ft. and would be 3/8" thick. Doing the math, we would need 466 sq ft of tile to fill the 14.6 cu ft of wall cavity. Price would be $10 for the insulation, and $742 for the tile - the tile is 74 times more expensive. Even if you don't fill the cavity entirely ( don't think R11 would ), it would still be much more expensive.
Tile is also much heavier. Depending on your construction methods, you wouldn't be able to use sheetrock for the wall sheathing. This would also pose problems for upper floor walls.
The other answers are good, but you might also want to consider the effect this will have inside the room. Tile will prevent sounds from entering the room, but it also is very reflective, so the sounds inside the room will echo around. Mineral wool absorbs the sound going both directions, so it will be quieter inside the room. If the goal is too achieve and overall quieter room, mineral wool will give you better results.