500 Ohm
500 Ohm
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 15 PA DJ Raw SubWoofer Speaker Replacement PRO Audio  US $57.50
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How can I power a 4 ohm dual voice coil subwoofer with the Rockford Fosgate 500s amp?
Im kind of a noob when it comes to dual voice coil subs. The sub is a 500 watt Alpine Type R 12" which runs at 4 ohms for each voice coil. The amp puts out 125 watts x 2 @ 4 ohms, 250 watts x 2 @ 2 ohms, and 500 watts @ 4 ohms when its bridged (i dont think its stable to be bridged at 2 ohms). I realize i should have gotten the 2 ohm version of this subwoofer, but its too late. I dont want to settle for 250 watts of bass because this sub is meant to take twice that much power. Is there any way i can get 500 watts going to this sub without buying a new amp?
No, you can't use that amp with that sub for a 500-watt output. Your best bet is a mono amp that will produce 500 watts at 2 ohms, or (as you said) the dual 2-ohm version of the Alpine sub.
If your purpose with the subwoofer is to have a decent bass response that's balanced with the rest of your system, then try it out; you might be perfectly happy with the subwoofer's performance at 250 watts. The difference in volume between 250 watts and 500 watts isn't as great as you might think. Unlike what some will try telling you, you won't be endangering your subwoofer by connecting it to a 250 watt amp.
I'm familiar with the link in Kicker_guy's answer. I don't disagree with anything in it. But there's nothing in it to support his 20% drop in power handling idea. If you use only one voice coil on a dual voice coil sub, its power handling capacity is cut in half. This is one of those cases where the common sense answer is also the right one.