Accidental reversal of speaker wires can happen when the wires are not properly labeled for polarity. This action is known as making the speaker "out of phase," and results in audio oddities. Although this is not dangerous to a speaker or amplifier, proper power delivery and speaker response is not possible with reversed speaker wires.
Bass response always suffers when polarity is reversed. Bass tones are generated in part by the pressurization of the air in the space surrounding the speaker. When the signal is out of phase, the bass speaker moves in when it should move out. Bass drum notes become virtually inaudible, and the music loses its muscularity and impact in the process. A simple swap of leads at the speaker or amplifier can remedy this.
Imaging occurs when a pair speakers successfully "projects" an audible representation of the instruments in front of you. When a speaker is wired out of phase, this information becomes out of focus, and sonically disorganized. This is especially true since the other drivers in the speaker cabinet are affected. Mid-range frequencies are present in the bass and tweeter drivers. Reversed wiring causes dynamic stereo information to "collapse," making the music lose much of its impact.
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High frequencies lose their focus when a speaker is miss-wired. This results in an "airy" treble that causes the sound stage to sound larger (yet less defined) between the speakers. Although some desire this, it is inaccurate in the strictest sense. Remember that all drivers are effected by this, so this brand of high-frequency response also comes with a poor imaging and thin bass penalty.
Typically affecting a pair of bass speakers in close proximity, cancellation occurs when the frequency of one speaker that is in-phase destructively competes with that same frequency of the opposite polarity -- produced by a nearby speaker. The result is that no bass is heard. This is a common error in automotive sub-woofer installations, when the two speakers are inches apart in the same enclosure.