10*20*? 8?
With 1/2 in MDF you want to either add a lot of bracing, or dble up the MDF by sandwiching it together. (Gorilla glue is good for that) or go 3/4 and run a cross brace. This will keep the box from resonating and amplifing the pump sounds. (once sealed)
Not sure where I got the idea that you were tring to make it as small as possible.
Assuming it is really loud...
www.partsexpress.com.
look for speaker spikes, (keep the box from vibrating the floor.may not be necc.)
acousic foam. (looks like egg crate, should be the same stuff your dad has in the studio.)
get some hurricane, or T nuts, or someting similar
you're gonna need to be able to get into the box from time to time. MDF does NOT hold up well to multiple screwings. you'll need lots of clamps, or screws. drywall screws with pre-drilled holes work wonders. You'll basically be making a small subwoofer box with a removable lid and places for tubing.
build 5 sided box. (simple box joints are suff. Just make sure they're square)
add damping material
roofing underlayment, (looks like foil coated tar. It's basically Dynamat without the price tag)
or dense foam (anti fatigue matt could work, even the cheap stuff at the auto stores.)
add acoustic fom to help with amplified reflections. (may not be necc)
make top (don't forget damping layers) that can be removed for access. (screws and wing nuts?)
veneer with you favorite wood.
or paint. I would suggest sealing the MDF before painting. you'll save a lot of pain as MDF really suck it in if it isn't sealed.
It may work pretty good. Then again, you may be building a one note pump speaker.
(edit: finished post. Stupid dog stepped on the keyboard.)