Reading back to the beginning of this thread I found the above remark. Is that a passive subwoofer or an active one?
In case of a passive subwoofer my remarks in post #7 with respect to powering the subwoofer are still valid.
In case of an active subwoofer your circuit diagram is misleading. In such a scenario you wouldn't switch the audio signal by the relay, rather the relay would switch the power to the subwoofer. Many active subwoofers have such a circuit built into them to save power when no signal is present.
In this case the relay module will not only have to detect the audio signal, it will also need to have a timer to bridge gaps in the audio signal for a few minutes. That prevents the subwoofer from turning off an on repeatedly during breaks in the music (between tracks, when changing disks, ...)- Here's an
example of a module for this exact purpose. Or a
circuit diagram for a DIY module if you are inclined to build one.