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I was putting a speaker into a new box and had to cut the plug off to take it apart. Now I'm not sure how to reattach it to the transformer. I can twist them back together without knowing the polarity right?
Depends what you mean by a 'transformer', a transformer is AC in AC out, so not polarity sensitive - a 'power supply' is likely to be AC in and DC out - but you haven't really given enough information on what you've got, and what's cut off.
Are there two speakers? stereo
If there is only one speaker then it does not matter. If stereo then the speakers need to be the same.
Are there more than one speaker? Base/mid/tweeter If 2 or 3 speakers then it does matter.
(assuming the wires are from a transformer to the speaker)
It appears the transformer is for power not audio. "120V 60hz" So the two red wires can be connected any way you want.
Some speakers have a transformer for audio. "4 ohm, 8 ohm, 16 ohm" In that case it will matter.