What's the best house wrap to use underneath hardiplank (fiber cement) sidings?
Make sure you install your siding according to ALL the manufacturers instructions, including the house wrap. See the Hardi specifications.
If you notice, the third item under “General Requirements” requires you to use a house wrap that is approved by the Building Department...which includes “HardiWrap”.
Using HardiWrap will assist in your sound control issue too. HardiWrap has small protrusions across the face of the moisture barrier which keeps the siding slightly away from the wall and allows moisture to “drain” down behind the siding. This “space”will help the STC rating of your wall...although I doubt the wall is the “weak link” in your sound control system. (I’d look at lack of operable window flashing, outlets on either side of the wall, etc. that create weak links in the sound control barrier.) There are some exceptions, like in very cold climates where the water can freeze and expand, so that’s why they say “approved by the Building Department”.
We know siding leaks, that’s why we use house wrap. We’ve now learned that water must escape too. So, the manufacturer now requires caulking at the jambs and sill, but not at the head of doors and windows. This allows water to run down the wall and escape and not get trapped at the head.