# Inverted Phase

Let’s demystify what phase is. We begin first by discussing time.

Time is usually used as a counter, to count the length of time to perform a particular task, e.g. 3 hours to roast a pork belly, or 10 hours from point A to point B. However we can also use time to track the life cycle of an event, e.g. the change from day to night, the changing seasons, high/low tides and so on.

In the first instance we are using time like a ruler, measuring a quantity known as time (function of time) like placing a piece of a string against a ruler to find it’s length. In the second case we are using time to describe the property of periodicity (function of frequency). In this second example, think of time the hands of a clock rotating around in circles. The number of rotations don’t really matter per se. For a clock, what is important is where the minute and hour hands are on the clock face.

### Relationship of Time And Angles

Below is a picture of a sine wave. Time is the X axis (horizontal bar with the label Time, t). There is a simple reason why we use degrees as our unit of measurement is simple. Waves have a unique physical property - at a certain point in time, the wave will revert to it’s original state and repeat itself. In other words, when the wave reaches 360°, the counter is reset to 0° and the whole process starts again. Like a clock striking midnight: a new day beckons, a new cycle begins.

The graph above (Credit: Wikipedia) is like unwrapping the circle of a clock into a straight line. If you extend the wave beyond 360°, the amplitude of t = 15° will be equivalent to t = 375°, 360° = 720°, and so on. This wrapping phenomenon is the reason why we use degrees. A picture speaks a thousand words, an animated GIF even more.

We only need to concern ourselves with waves when t=0°, and t=360° due to this cyclical property. The time taken to complete a cycle is called the period (T) of the wave (with the units of seconds). To get the angle, we divide this T into 360°. Anything beyond T are simply multiples of T - 0° to 720° is 2T, 0° to 1080° is 4T and so on. By focusing just on T, we are effectively breaking a big problem down into a smaller and simpler problem that’s easier to solve.

In audio, it is preferable to use the unit frequency (Hz) instead of period, frequency is really 1/T and is the preferred units because we are dealing with shorter periods in audio. The two units are interchangeable and which unit to use depends on the physical application. e.g. In oceanography, waves have longer periods and thus people prefer to use periods instead (i.e. this is a 20 second period rather than 0.05 Hz wave).

A cycle is where a wave cross the Y=0 mark as shown above. One important note is this Y=0 is the zero crossing and not necessarily a numerical 0. In the physical world, this zero crossing is usually the median value. All measured values are normalised to this median. What this means is all physical measured values have the median subtracted. Any value greater than the median becomes positive, any below becomes negative, and the median is the new zero.

So what is phase then?

In the context of this article, it’s the starting angle (along the X-axis, time) where the wave begins relative to a reference. And in the case of audio, the reference is anywhere when Y = 0 (0 voltage).

Think of phase as asking the question of ‘*does it line up*‘? If your system is wired correctly, the phase will be 0° (this means in phase), and the phase is 180° if wired incorrectly (referred to as out of phase).