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 zerocrossing points (Z) of both waves all coincide. The phase difference of the waves is thus zero, or, the waves are said to be inphase.
If the two inphase 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 zerocrossing 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 outofphase, 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 zerocrossing point (Z) on D, a zeropoint 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.
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