You could consider this as a trade off between marginal sound abatement versus ease of retrofit for any future access need in the stud bay, whether for wiring (say you add computer cabling or HVAC zoning, new 120 outlet,etc.
Of course, insulation isn't too hard removing for some jobs, and it does pay off for both HVAC and sound abatement, which you won't like when you're older,going deaf and yelling to someone not in the same room.
By backing I assume you mean vapor barrier. Don't need it on interior walls. Either of the R values R OK.

It doesn't really help that much with sound. We just did the downstairs powder room - I think that cost $100. If sound ever was an issue - you could retrofit another layer of drywall which I believe actually works better.

Put sound insulation between the walls, but more importantly, mount the drywall on resilient metal channels. We have done it, and it really cuts down noise transmission between adjacent rooms.

Our existing house has interior insulation. It is very quiet, with little noise transmission between floors or rooms. I have no idea if it has the resilient channels or not.

I posted a very similar question on this forum a few days ago (see postings from last week) and I received some extremely useful information posted in response.

In particular, one of the experts on this forum posted a chart that compares the effectiveness (in dampening sound) between various materials including insulation, an extra layer of drywall and resilient channels. It was clear that interior wall insulation only helped slightly, while both extra drywall and resilient channels were more effective.

As a result, I tried to have our contractor put another layer of drywall in a couple of the rooms, but it was far too late to do so. The contractor told me that, at this point (insulation is in, drywall about to begin), putting another layer of drywall would mess up the amount of space left for electrical and other things, since everything was already calculated for 5/8" drywall. If I had to do it over again, I would've planned that part more carefully and put extra drywall around some bathroom/bedroom walls to lessen sound transmission.

Again, I'd encourage you to look back at posts from last week and see the chart that was provided by a poster (cut and pasted from the Journal of Light Construction) which contains hard data specifically spelling out the difference between various construction materials in lessening sound transmission.

Best of luck.

Thanks so much for everyone's opinions. For $120 and an afternoon worth of work, we decided it was worth a shot, so my husband got it all done yesterday and drywall is going in today they tell us!

Wildcat, A respected member of these forums,(Worthy), always advises to use solid core doors on the interior cut as close to the flooring as possible to help deaden sound. You might consider that when picking out your interior doors.

cut as close to the flooring as possible to help deaden sound.

Yep, I do say that. But I should add the caveat that this assumes you have a well-designed HVAC system that doesn't depend on undercuts and multi-room returns, but is instead completely ducted. Ducted returns can also be designed to reduce sound from the HVAC system. But keep in mind that lined ducts are on Dr. Joe Lstiburek's Ten Dumb Things to do in the South.

susan3733
Your contractor is making up a reason to not put a second layer on instead of explaining the real reason (whatever that may be). It doesn't matter if the outlets have been set for 5/8 GWB, they can have extension rings added. It is only when the trim is installed that adding another layer becomes a problem.

mightyanvil,

The contractor said we couldn't do it because "everything was already set" for 5/8 drywall, whatever "everything" is. When I tried to question him further, he specifically mentioned electrical. Could adding another layer of drywall in the powder room also impact plumbing and/or electrical fixtures (in addition to electrical outlets)? Are either of these issues particularly time-consuming or expensive to fix?

This is typical of my contractor, who seems to frequently have a knee-jerk "no" response instead of helping develop a solution. I can understand if it was going to be a major hassle or time-consuming or expensive, but that's usually not the case...it's like he just can't be bothered and will even make up an answer to avoid having to give it a second thought. Very frustrating.

Many thanks for your continued advice.

Susan