Reversing Polarity -- Voodoo or Easy Tweak?

When I said "equal but opposite polarity" I meant equal amplitude but opposite polarity.

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To be a total stickler for terminology, speakers CANNOT have their polarity reversed, since they are driven by AC, which has no + or - poles! Only DC has a + or - polarity. Speakers can have only an absolute phase inversion [both speakers have the wires reversed on the + and - terminals], out of phase [only ONE speaker wire will have the + and - terminals reversed...very bad indeed!], or have a phase shift. A phase shift occurs when different frequency ranges are shifted [delayed] by milliseconds. This can be due to crossovers, physical driver alignment, speaker wires, or the amplifier powering the speakers. Sort of like a prism splitting white light into the various frequencies of colored light...in effect, a rainbow. Again, not good. But phase shift is pretty much a fact of audiophile life. The amount of phase shifting will determine the coherency [or not] of the sound.

FYI, here's a neat trick to get raw drivers in phase when the terminals are not marked or marked incorrectly [it does happen!], or for car installations where multiple long concealed speaker wire runs can easily be installed out of phase. Take a "D" cell battery, and hold the speaker wires to the battery. Note whether the speaker cone moves out or in. I consider "out" to be the + terminal and "in" to be -, this being a good memory aid.

Herman...You are a bit hasty in saying that the drum sound will be compression followed by rarefaction. It depends on which side of the drum the mic was on. Also, as a disturbance propagates the wave shape changes. Consider, for example a Tsunami, where the initial disturbance is always that the sea recedes, followed by the flood. I have observed a similar effect of a ship bow wave while going through a canal. There must be an explanation, but I don't know it.

Do you have any scope pictures of a mic signal from a drum?

I see we are still confused, and I don't blame anybody for being that way since it is a bit confusing even without the years of improper use.

AC, which has no + or - poles! Only DC has a + or - polarity. Speakers can have only an absolute phase inversion

This is incorrect. Absolute phase inversion makes no sense. I know what you mean, but it is an incorrect use of the term phase. Phase has to do ONLY with time, and you cannot invert time.

AC does indeed have a polarity at any given given point in time. It may be incorrect to say that a given AC signal is overall positive or negative, but at some points in time it is positive and sometimes it is negative.

A clear example is a balanced system. You have 2 signals. One is the same as what a single ended system would have, and the other is inverted. This second signal is also commonly described as being "180 degrees out of phase" with the other one, but it is not. It's polarity is inverted, not it's phase. In a sense they are mirror images of each other.

When one is going more positive the other is going more negative.
If one has a value at a given point in time of +2 volts and headed more negative, the other one will be -2 volts and headed more positive. As an aside, I see this as a major problem with balanced systems. They must take 2 signals of equal amplitude but opposite polarity and amplify them through 2 different chains of amplifiers with the exact same gain and phase shift in both chains.

A phase shift occurs when different frequency ranges are shifted [delayed] by milliseconds

This is correct. Speaking to Eldartford's earlier point about the phase shift in crossovers being inconsequential, I disagree. At the -3dB (half power) point of a first order filter the phase shift is 45 degrees. This is a significant amount, especially if the fundamental frequency from an instrument falls in the passband and the first harmonic falls outside.