Vocal Booth in Spain

Hello to all. At first, sorry for my english. We are a beginners in this and we are from Madrid, in Spain. This is the thing. I'm now in the design phase of the project, and I look isulation and woods, but in the original concept, I think in two diferent frames without contact.

In the images, the measures are teorical, because I depend of materials. My question is about the system that I choose to make the vocal booth. Look the images, In red is the internal frame, the blue next to this frame, is compressed wood. The yellow and green are isulation fiber. In brown is the external frame and the last part in blue is wood too. In the pictures don't see, but in the floor I think in put silentblocks. My question is: Is the better way to do a vocal booth? what kind of troubles I have with this system?. I try to read all the topics in the forum, but my english is poor and I don't understand all. Can anybody tell me some topic who speak about this thing? My idea is arrange the system and next make the final project with the measures and materials. Thanks for your time. Best Regards. Alfonso Generoso.