Phase & Polarity: Causes And Effects, Differences, Consequences
The terms "polarity" and "phase" are often used as if they mean the same thing. They do not.

The “Glitches”
The glitches in figures 6 and 8 give an indication of what happens during the onset of a signal. While the so-called steady state portion of the combined signal (shown by the black portion of the lines) looks the same except for the amplitude change, these glitches will affect the transient attack of sounds. This is not to say that either will sound horrible, but a phase shift between otherwise identical replicas of a sound WILL make a difference in the sound of the initial transient attacks, depending on the frequency and amount of phase shift.

This is exactly the kind of phenomena that can occur in the crossover region of a speaker. This is because the distance from each driver to the listener is usually different and the crossover itself shifts the phase of the signal between the drivers. Speaker designers are often faced with a choice between something like what you see in figures 6 and 8. Neither is “correct” so a designer can only choose the one that “listens” better. Just looking at these two, I would bet the waveform in figure 8 might sound better and the choice would be to reverse the polarity of one of the drivers. These crossover “glitches” occur only over a small range of frequencies where both drivers reproduce the sound. It is well accepted by designers that this kind of “improvement” is sonically more significant than the fact that frequencies above and below the crossover point may be out of polarity.

Signal Phase Shifted 180 Degrees
This is where many get into trouble in thinking that phase and polarity are the same thing, meaning that it is often assumed that a 180 degree phase shift and reversing the polarity are the same.

Figure 9: In this figure each sine wave lasts for only 2-1/2 cycles. The second sine wave, shown in red, is shifted in phase 180 degrees from the first shown in blue. This is what would happen if the speaker reproducing the red sine wave were about 6.8 inches (170 mm) further away from you than the one reproducing the blue sine wave. You can see that between the 180 and 900 degrees the signals LOOK like they are simply out of polarity but they are NOT. It is VERY important to note that if you could not see the beginning or the end of these signals you could not tell whether they were out of polarity or 180 degrees out of phase. Too often this is what causes confusion between a polarity reverse and a 180 degree phase shift.

Figure 9: Two Sine Waves - Red = Phase Shifted 180 Degrees & Polarity Reversed.

Figure 10: This is the result of combing the two signals. Unlike figure 4 where the signals are simply out of polarity, and completely cancel, there are clearly two positive halves of a sine wave visible before and after the two signals cancel along the black line between 180 and 900 degrees. The first is from the blue sine wave in figure 9 that occurs before the start of the red sine wave. The second is from the red sine wave in figure 9 that continues after the blue sine wave stopped.

Figure 10: Sine Waves in Fig. 9 Added.

Signal Phase Shifted 180 Degrees And Reversed In Polarity

Figure 11: This is the same as figure 9 but the polarity of the red signal is reversed from figure 9.

Figure 11: Two Sine Waves - Red = Phase Shifted 180 Degrees & Polarity Reversed.

Figure 12: This is the two signals in figure 11 combined. Between the 180 and 900 degrees, the signals add much like in figure 2. However there are significant differences in the overall 90 to 1080 degree signal. The first 1/2 sine wave of this signal is only from the blue sine wave from figure 11. The last 1/2 sine wave is only from the red sine wave in figure 11. You can clearly see that both of these 1/2 sine waves are only 1 volt at the peaks. This is a clear difference from figure 2 where all the peaks reach 2 volts.

Figure 12: Sine Waves in Fig. 11 Added.

The reason is that the two signals in figure 11, even though identical, are offset by 180 degrees. They add together only between 180 and 900 degrees when both are being heard. More importantly, during this time period DIFFERENT parts of the same signal have added together. For example you can see that between 180 and 360 degrees it is the second 1/2 of the blue signal’s first complete sine wave that adds to the first 1/2 of the red signal’s first complete sine wave.

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