The first kind is sound transmission through the air and the material that Jay suggested is great for that. Also, plug all holes and air gaps.
The second kind is sound transmission through a structure and the double wall is good for that.
Both types of sound treatments should be considered for effective noise isolation. It is actually a very complex subject but you will be way ahead of the game if you keep these two things in mind.
I forgot to mention -- if the two offices share ductwork then there's only so much you can do without attcking the ductwork problem as well. Good luck!--Billy
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