Audio Systems: the best amp for my sub, sony xplod, watt amp


Question
The box is 15 x 15 x 17. And its got a big hole in the front where the sub goes is, and a little in the back for the wires...But the sub is screwed into it also...If that helps.

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The box was made by a friend with MDF wood. So I'm not sure what it would be considered. And the sub is a Sony Xplod 1200 Watt. I've heard that they are known to blow fast by some people, but others haven't had a problem with them. There really isn't a budget I'm looking for, maybe anything under $200, but thats not definite. I mean I would like an excellent amp for cheap of course but I'm not expecting to find a really good one for like $50.

But basically what you are saying is that I should look for an amp thats 400-500 watts?
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Ok I have a 12" subwoofer, the specifications are:

Peak Power - 1200 Watts
Rated Power - 350 Watts
Ohms - 4 ohms
Sensitivity - 89 dB/ W/ m
Frequency Response - 18 - 2000 Hz

And I was wondering what would be the best amp to use with it. Like what wattage should I look for, or whatever. And also should I get a capacitor or not.
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some of picking the right amp also has to do with the box its in, sealed/ported/bandpass size and tuning of the box etc.  but basically you're going to want an amp whos RMS power matches the RMS rated power of the sub at the same ohms of the sub.  Its usually ok to go a little above the rating since clean power is safer than dirty power, in other words, your sub is rated for 340 watts. if you get a 300 watt amp and crank it all the way up will will distort, this distortion can blow the sub even though it's only 300 watts and your sub is rated for 350. so in my opinon it's better to get like a 400-500 watt amp for a 350 watt sub so that when you turn it up to 350 watts its still clean power and wont blow your sub.  make sense? it would be nice to know who makes your sub since some manufacturers under rate and some overrate.  like if it's made by boss audio or one of those cheap companies I would stick to the rated power and not go over it, but if it's a decent brand you'll be fine to go over.
you didnt give me a budget either so I dont know if you want the best 400 watt amp money can buy or the best bang for the buck 400 watt amp money can buy.  but oh well...
Rockford Fosgate is having a year end sale right now to make way for new models so they're real cheap.  The punch P4002 is rated for 400 watts into a 4 ohm load and they're going for about $120 on ebay right now.  the punch P5002 is 500 watts which I think would be fine on your sub and that one's only like $140 so that would be my pick.  
I wouldnt go over 500 watts even if it's a good brand since you'll have the chance of overexcursion or over heating the coil at that point.
If you want to write back and tell me more about the box and the make and model of the sub I'll confirm or change my recomendation for ya.
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ok, as for the box, does it have a big hole in it or just the sub (ported or sealed)  do you have any measurements of the box?  
I think either the 400 or 500 watt amp will be fine and it looks like I picked stuff that's well within your budget too. You just need to listen to it as you turn it up.  you'll get to a point as you're turning the sound up where it doesnt get louder, it just sounds awful, if you hear this, back it down IMEDIATLY or it will blow. the people that blew their subs probably got small amps so when they turned it on it wasnt that loud cuz of the small amp. so they cracked it up as high as it could go, this caused the distortion that blew the sub.  that's why I'm recomending a bigger amp, but you still have to be careful it doesnt distort or it will blow anyway.

Answer
ok well if there isnt a tube in the box or a large slot hole in the side then it's a sealed box.  a sealed box really needs to be sealed air tight so if the hole in the back where the wires go has space around the wires get a tube of silicone rubber and fill it all in so it's airtight or that can damage your sub and sound awfull as well. if there are any gaps around where the sub is screwed in put the sealent there too.  in fact if the box isnt carpeted (the carpet makes a good seal for the sub) so if it's NOT carpeted do yourself a favor and unscrew the sub and put a bead of the silicone rubber all around the edge of the hole and screw the sub back in so it's sealed airtight to the box.
now for the size and amp, if the box is 15x15x17 on the outside and your fried used 3/4" thick MDF then internally the box is 13.5x13.5x15.5  which comes out to 1.6 cubic feet.  I would go with the rockford fosgate 400 watt amp in this box. if it were smaller then you'd need the 500 watt amp but 1.6 cubes is a medium large box for this sub.
Good luck and let me know how it goes.