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Thanks for the mention @Jason 
My apologies for the delay in replying @Lucille.
'Soundproofing' is certainly done in Australia - and definitely as a DIY project - but not in terms of a 'DIY foam core kits that can be sprayed between the framework'. I haven't heard of anything like this...and regardless it would not suit gypsum board walls (typically called plasterboard in Australia...but the same stuff as American 'dry wall'...just in metric measurements 
)
From the top of my head I can think of two solutions...but neither are all that appealing!
Either:
1. Remove one side of the plasterboard and install insulation 'batts' - there are a number of differing types and sizes depending on the existing wall and what you want to achieve - then replace the plasterboard (will require new plasterboard to at least one side of the wall, along with patching, painting etc.). Not ideal...
2. Depending on location you could add 'steel channel' and/or 'resilient clips' to the wall(s) and put plasterboard over these...again less than ideal; and if you have an existing 'empty cavity wall' then you risk possible 'triple leaf effect' with this approach.
Don't worry about what 'triple leaf effect' is...really option (1) is about all you can do...UNLESS...
You can specify what you are actually hoping to achieve...? 'Sound proofing' is a vague term; actually it's the wrong term. Inside the realm of acoustic sound treatment it is not really used. It is split into two concepts which are 'sound isolation' (stopping sound from coming through a wall) and 'sound treatment' (this is where the cool egg crate foam comes in ). Depending what you want to achieve (and how much money and time you are willing to invest) there can be different approaches.
The options listed above are really just two possibilities that I have given (whilst making a pile of assumptions!). If you can specify a little more about the walls condition etc. I might be able to help more...?
Hopefully some of that made sense...? Haha...I am halfway through my own 'sound proofing' project...and I think most DIY'ers can relate to that stage where a few things have gone wrong and a few have been tedious...and you want to headbutt a wall to take the pain away? 
yessss...I am about there at the moment! Thank goodness for single malt...
Cheers
G'day @MartyH
Yes that is a good point...I guess 'insulation' is normally thought of more in terms of it's thermal attributes. However:
My houses internal walls made of the gypsum boards are empty inside!
I am not familiar with thermal insulation being done to interior stud walls...? I live in Perth WA and I can't recall having seen thermal insulation in stud walls...please let me know if you have experience with it and know more than me!
If the OP is solely after treatment of sound issues then regular (thermal) insulation would be the wrong thing to use; it is not designed for an acoustic environment. Dependent on what they wanted to achieve they may be able to use thick curtains, acoustic foam, bass traps, abosrbers and or diffusers, and many other things that wouldn't need to involve accessing the cavity at all.
Cheers
