Are thicker cables more effective for subwoofers?

Yes they are. The sub needs thick cables both for optimal power delivery but also for tight bass. Skinny wires will make bass loose and sloppy.

Without knowing the power of the amp and the speaker impedance, we cannot say what wire size you need but 12 Ga is a good start. For a 1000W amp driving a 1 ohm speaker, we would use between 4 Ga and 00 Ga.

it's totally dependent on the specific application. It's an issue mainly of current, and also voltage drop which are a result of power, impedance, and length of the wire.

As long as the wire is adequate it doesn't improve anything to go larger.

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