I am testing out different materials with different specific heat capacities and their correlation with soundproofing (e.g. wood, cork, styrofoam, etc.) but I can't seem to find the specific heat capacity of cardboard anywhere (the average S.H.C. of regular corrugated cardboard).
I don't think the specific head capacity matters much when you are trying to do sound insulation. Characteristics related to sound interactions matter more, like shape, or sound propagation.
Here is lots of info: I have no idea why I spent time answering this question.
Substance Specific Heat - cp - (J/kgoC) Cellulose, cotton, wood pulp and regenerated 1300 - 1500 source
The heat stored is then cp(cb)*M(cardboard)*T(K)
Paper cp= 1336 J/(kg*K) location of cp
Corrugated cardboard is a stiff, strong, and light-weight material made up of three layers of brown kraft paper. In 1884, Swedish chemist, Carl F. Dahl, developed a process for pulping wood chips into a strong paper that resists tearing, splitting, and bursting. kraft paper
Kraft. Kraft comes from the German word meaning strong. Kraft paper is made from at least 80% sulfate wood pulp. It is course and exceptionally strong, making it well suited for a packaging substrate. Composition
What the other 20% is is hard to find. The essential elements for making kraft pulp are wood fibre, water, chemicals and heat. Source
"carboard" is no such thing - I assume that you are referring to Corrugate = Kraft Liner Board with a Kraft Flute medium. There are many more reliable materials for soundproofing than corrugate.... though there is liner with foam fluting/face stock. If you're stuck on corrugate, remove one face liner to expose the medium - this will give you the sinusoidal configuration to bounce your sound waves.