What would you have in the enclosure that would hum? Besides the singer, of course!
If it's 60Hz hum ... that's a grounding problem ... not acoustics/soundproofing.
Because you're building a square room, you might encounter some problems with resonant frequencies. Foam will help with this, but maybe a rethink on the room dimensions might be better.
Check out the products and especially Acoustics 101 pdf document at this site:
I don't give this site to promote their products ... but more because it's the only place I can find online that gives nice diagrams of the concepts without a whole lot of blah-blah-blah on the physics of them.
You don't have to buy any Auralex stuff to take advantage of the good ideas and practices that they have there. For example, before you build your walls for the enclosure, you can compare the different construction configurations they outline and weigh the STC ratings against the potential cost for your specific situation.
Anyway, don't know if that helps or not