How can I transform 12 Volt DC to 17 Volt AC?
It's pretty certain that the amplifier (we're not talking about the subwoofer as speaker, we're talking about the amplifier – the subwoofer itself is passive, ie. just the thing that converts an electrical audio signal directly to air pressure changes) internally uses DC.

You'll very likely find a diode bridge rectifier right after the point where the 17 VAC enter the PCB. Probe the DC voltage at the big capacitors coming after that rectifier! That's the DC voltage you'll need to supply.

If that voltage is not 12 V (and it probably isn't) you'll either need a step-down converter (target voltage &lt; 12 V) or a step-up converter (target voltage > 12 V). It's not terribly hard to build one, even for audio applications with OK noise properties (especially since your subwoofer won't even care about noise >1kHz at all).

Now, big speaker systems do need quite some power. Your transformer is rated for a little more than 40 W (effective voltage * current) – that probably leaves some headroom that you won't fully need, but it's still going to be a relatively solid power supply you might be building. 

If you're lucky, the rectifying circuit is designed in a way that gives you close to 12V as target voltage, or just a few volt above. In that case, simply remove the transformer and directly power with the battery (at the point where you probed the voltage).

All in all, as said, the PCB looks dated. That means the amplifier is probably of a "classical" design – which might be a very good design in some respect, but it guarantees that it's not very power-efficient. In your case, that's bad for two reasons:


your battery won't last long, and
your step-up or step-down power supply need to be capable of providing more power.


In effect, it might actually be easier to get a bare-PCB class D/E amplifier that directly works off 12V – I, for example, use exactly such a device to power speakers when going on festivals. They're available for a couple of bucks on the usual websites.



Edit

With your photo of the power supply PCB, we can be more detailed:



You correctly labeled the Diodes already!

The circuit they form is this:







simulate this circuit &ndash; Schematic created using CircuitLab

The component numbering doesn't necessarily match your board (can't see how the traces run under the diodes). Notice that the big "cylinder" right of the diodes is probably the capacitor I keep mentioning.