I don't know how to tell you, but you really don't want to use carpet in your studio on the walls like that. You ask what frequencies they'll absorb? All the wrong ones. They'll soak up the high frequencies but will do just about nothing for bass frequencies, leaving your room sounding very bassy. This will make you turn down the bass in your mix, and then your mixdown, when played outside your control room, will sound very low-end empty.
How to put it in your vocal room? I wouldn't use carpet at all in a room that you're going to be doing so much micing. In a room where you're trying to translate the sounds SO accurately, carpet will give your room a very bassy sound. But if you really want to use it at all, use it on the floor, and NOT the walls. The small, tight size of the vocal room will already give it a very bassy room mode, don't make it worse by putting carpet in it.
You say you can get carpet for cheap... well I bet you could obtain some decent studio foam, that is manufactured to absorb the correct frequencies, for the same price as the carpet.
In my studio the only place we're going to be using carpet is the drum stage, and we're going to be using heavy industrial carpet, and the only reason we're using carpet is because if you don't drums like to scoot across the floor. Not to mention they'd ruin hard wood flooring.
Later,
-Brian