Interference Interference

INTERFERENCE:
The combining by superposition of two or more waves that meet at one point in space.

SUPERPOSITION OF WAVES:
When two or more waves interfere, the resultant wave's amplitude equals the sum of the signed amplitudes of the interfering waves.

CONSTRUCTIVE INTERFERENCE occurs when waves interfere in such a way that the amplitude of the resulting wave shows positive growth.

DESTRUCTIVE INTERFERENCE occurs when two or more waves interfere in such a way that the amplitude of the resulting wave shows negative growth.

The following more specific cases of constructive and destructive interference are important in the explanation of the interference of light and the single slit diffraction pattern.
Note that the period, wavelength, and amplitude are the same for all the original waves.

IN PHASE: Here wave 1 and wave 2 are said to have a phase difference of 2p, or simply are in phase, because both waves have the same wavelength and rise and fall together. Any two waves with a phase difference of a multiple of 2p are in phase.

This leads to constructive interference, and the resultant wave's amplitude equals the sum of the individual wave amplitudes. Here, the resultant amplitude is twice as large as wave 1's (or wave 2's).

OUT OF PHASE: Here wave 1 and wave 2 are said to have a phase difference of p, or simply are out of phase, because wave 2 looks like wave 1 shifted half of its period to the right. Any two waves with a phase difference of an odd multiple of p are out of phase (p, 3p, 5p,...).

This leads to deconstructive interference, and since wave 1 and wave 2 also have the same amplitude, the waves completely cancel each other out and the resultant wave has an amplitude of zero.

And of course it is also possible for two waves to have a phase difference other than p. In that case, the resultant wave's appearance is somewhat more complicated, but found according to the superposition of waves, defined above. There will be both constructive and deconstructive interference.

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