Ok here is another srticle by the biggest guru in our biz. Complete article here http://mixonline.com/ar/audio_understanding_phase/
PHASE AND POLARITY
Before we move to the next section, time for a pop quiz. How many milliseconds of delay results from 180Â° of phase shift?
Is that your final answer?
The correct answer is, â€œThat's a trick question.â€ Why? Because a frequency must be specified. So how many milliseconds of delay are equivalent to 180Â° of phase shift at 250 Hz? The answer is 2 ms.
Now, how much time delay do we get when we put a phase reverser in-line? It reverses all frequencies by 180Â°, so it must delay each one by a slightly different amount. That is quite a fancy delay circuit there! And I thought it was just swapping two wires! In reality, there is no such thing as a â€œphase reverser.â€ It is a polarity reverser. Polarity reversers do not delay the signal. They invert the voltage or pressure component of the signal. While this does shift the phase, it does not change the phase delay time. That is not to say that a polarity reverse is unimportant. Anything that affects the phase will dramatically affect the way that different signals combine.
When two signals of the same frequency are combined, the summed response may be greater than or less than the original signals, depending on the phase. One plus one equals two, one or zero if summed at 0Â°, 90Â° and 180Â°, respectively. In a speaker array, the amount of addition will depend upon how close to 0Â° phase difference there is in arrival times. The tendency of speakers to add or subtract is shown in Fig. 2, which illustrates the hemispherical nature of combination. Signals that combine on the 90Â° to 0Â° to 270Â° hemisphere will achieve constructive addition. Signals on the 90Â° to 180Â° to 270Â° side will subtract. Constructive addition is easily done at low frequencies where it takes path length differences of several feet to move out the speaker of the addition zone. The highs, like football, are a game of inches.
The relationship between phase and polarity is illustrated in the series of simulations in Fig. 3. In this series, two speakers are splayed 60Â° apart, and the response is viewed at 250 Hz. In 3a, the response of a single unit is shown as a directional pattern reference. In 3b, both speakers are enabled, and the response shows a beam at the center of the array where the speakers combined at 0Â° relative phase, yielding 6 dB of addition over the response of a single unit at that location. The sides of the beam are formed in the area where the speakers are 90Â° of relative phase apart, creating minimal addition. The nulls are caused as we move into the cancellation hemisphere, with the deepest spot being 180Â°. Side lobes appear where the signal is a full cycle (360Â°) out of time, allowing addition to occur again. At different frequencies, the position of the nulls and side lobes will change. The time between the cabinets stays the same, but the change in frequency causes the relative phase to change.
In Fig. 3c, there has been a polarity reversal in one of the speakers. The amount of energy generated by the speakers is the same as before, yet where it goes has reversed completely. Now, the side areas contain the bulk of the energy, while the on-axis area is in a null.
Finally, in 3d, we have a delay of 2 ms on the lower speaker. This is half a wavelength at 250 Hz. The 2ms delay steers the sound downward toward the delayed speaker in the direction of where the 0Â° addition area is centered. (This technique can be used to optimize arrays, the subject of Part 2.) Compare this to the polarity reversal above where the signal is flipped 180Â° (half a wavelength), but the result is quite different.