Final answer:
Wedged foam is the ideal material for soundproofing the walls inside the game show booths, as it effectively absorbs sound waves and reduces transmission.
Step-by-step explanation:
The material that should be used on the walls inside the soundproof booths for the game show contestants is wedged foam. Wedged foam is an excellent soundproofing material due to its ability to absorb sound waves. When sound waves hit the foam, they get trapped within the wedged shape of the foam, reducing the transmission of sound into and out of the booth.
Wood panels and stainless steel plates are not effective in soundproofing as they are rigid materials that can reflect sound rather than absorb it. Using nothing on the walls would allow sound waves to freely pass through the booth, defeating the purpose of soundproofing.