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PHASE ROTATION
Sound is our ear's perception of waves of alternating air pressure traveling through the air, much like ocean waves are waves of water of varying heights traveling across the ocean. Via microphones these waves of air pressure are turned into waves of electrical voltage. (In the case of electric guitars, we have pickups detecting a wave-like motion of our strings and turning those into the electrical current.) The waveforms we have been looking at in our illustrations here and that we see in the timelines of are DAW software are visual representations of these waves of electrical voltage.
A common characteristic of all of these forms of waves is that they are periodic. This means that there is not just a single wave, but rather a series of similar waves, one right after another. The distance from the beginning of one wave and the end of that wave - which is also the beginning of the next wave - is called the wave's wavelength. Each wave starts at it's "sea level", or rest voltage (typically the 0V centerline, but it can be a DC offset voltage), builds up to a wave crest, dips back down to a wave "valley" and returns to the sea level rest voltage to make one complete wave. This forms a complete cycle that keeps repeating itself. This is why the frequency of a given waveform is measured in "cycles per second", a.k.a. "Hertz"; the frequency is how many times the wave rotates through a complete cycle in one second of time.
This cyclic nature of waves is why we measure their phase in degrees of angle. Just like a circle cycles or rotates around 360° of angle to connect back where it started, so in it's own way does a wave, starting at sea level or rest voltage and cycling through it's peak and valley only to return back to its original sea level/rest voltage. It's the same thing with the phases of the moon; starting with a new moon, and cycling through it's waxing to a full moon and then waning back to a new moon all over again some 29 days later.
This means that any point in a wave cycle can be said to be x number of degrees through that wave cycle. The start of the wave is at 0°, the end is at 360°. The end/360° point of a wave cycle is also the beginning/0° point of the next wave cycle, depending on how you wish to look at it. For a standard sine wave that rises to a crest before it falls to a trough, this puts the top of the crest at 90°, the point where the wave crosses the centerline on it way down to the trough is at 180°, and the bottom of the trough at 270°. For the phases of the moon, if we start with a new moon, the new moon is at 0° in it's phase cycle, the waxing half full moon phase is at 90°, the full moon is at 180°, the waning half-empty moon phase is at 270°, and the next new moon is at 360° or 0° of the next moon cycle.
For our waveforms, this can also be pictured (and mathematically often is pictured) by adding a third dimension to the graph, on the Z axis. The X axis already represents time and the Y axis already represents amplitude. Now we'll place a circle on the Z axis to represent phase angle. If we start with a phase value of 0° as being a point on the circle even with Y=0 - the 0V DC centerline - one can visualize rotating around that circle and rotating through 360° to wind up that the start of that circle again. As we rotate around the circle, rotating through phase, and we trace out that phase angle point on the timeline as we move through time (remember: cycles per second), we wind up tracing the picture of our familiar sine wave (see Figure 8).
Imagine looking at a spring something like the spring in your retractable ballpoint pen. When you look down the center of it, it looks like a simple circle. When you look at the spring directly from the side, however, it looks like a sine wave (see Figure 9). When you spin the spring around it's center access, the "sine waves" appear to move down the length of the spring. This is somewhat analogous to the rotation of the phase angle property of a wave as it occurs over time.
We should note that sound waves or their voltage representations in our audio systems are not physically three-dimensional like a spring; the third dimension of phase is a mathematical concept only. But it does provide a useful image to help in our understanding of phase.
Now, where this gets interesting is we can "spin" or rotate the phase of a waveform just like we can spin that spring around it's center axis. What this basically means is that we are moving the start of the wave from 0° to some new degree value. For example, we can rotate the sine wave by, say, 90° so that the wave now starts at 90° and rotates through past 360° and ends up back at 90° again. Figure 10 displays an original wave in green and the same wave phase rotated 90° in yellow. Note that there has been no actual shift of the wave's position left or right - i.e. there is no shift in time - just a pure and instantaneous change in phase angle of the wave.
In a pure coincidence of physics and geometry, a phase rotation of 180° results in a waveform that is a mirror image of the original waveform. This is why phase and polarity often get confused. But there are two important differences; the first being that phase rotation only creates an apparent "phase inversion" or mirror image if the rotation is exactly 180°. Any other degree of rotation will not create a mirror image. The second is that polarity has it's "mirror" at the 0DC centerline, no matter what. Phase does not.
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