Phase (waves)

Phase is the relative position of a feature over time. Examples of phenomenon where phase is an aspect of their nature include phases of matter, phases of the Moon, or one of several immiscible liquids, or the position of a peak or a trough of a waveform, compared to that same feature on a second waveform. The phase may be measured as a time, distance, a fraction of the wavelength, or as an angle in radians.

A phase shift is simply a difference or change in phase.

Consider the two waves A and B in this diagram:

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Both A and B have the same amplitude and the same wavelength.

It's apparent that the positions of the peaks (X), troughs (Y) and zero-crossing points (Z) of both waves all coincide. The phase difference of the waves is thus zero, or, the waves are said to be in-phase.

If the two in-phase waves A and B are added together (for instance, if they are two light waves shining on the same spot), the result will be a third wave of the same wavelength as A and B, but with twice the amplitude. This is known as constructive interference.

Now consider waves A and C:

A and C are also of the same amplitude and wavelength. However, it can be seen that although the zero-crossing points (Y) are coincident between A and C, the positions of the peaks and troughs are reversed, that is an X on A becomes a Y on C, and vice versa. In this case, the two waves are said to be out-of-phase, or the phase difference of the two waves is π radians, or half the wavelength (λ/2).

Should waves A and C be added, the result a wave of zero amplitude. This is called destructive interference.

Also consider waves A and D:

In this situation, a peak (X) on wave A becomes a zero-crossing point (Z) on D, a zero-point becomes a peak, and so on. The waves A and D can be said to be in quadrature, or exactly π/2, or λ/4 out of phase. This is the same relation that the mathematical functions sine(x) and cosine(x) have.

See also interferometer.