Interference

Interference is the superposition of two or more waves resulting in a new wave pattern. As most commonly used, the term usually refers to the interference of waves which are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same frequency. Two non-monochromatic waves are only fully coherent with each other if they both have exactly the same range of wavelengths and the same phase differences at each of the constituent wavelengths.

Constructive and destructive interference

When two waves superimpose, the resulting waveform depends on the frequency, (or wavelength) amplitude and relative phase of the two waves. If the two waves have the same amplitude A and wavelength the resultant waveform will have amplitude between 0 and 2A depending on whether the two waves are in phase or out of phase.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Consider two waves that are in phase,with amplitudes A1 and A2. Their troughs and peaks line up and the resultant wave will have amplitude A = A1 + A2. This is known as constructive interference.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

If the two waves are 180° out of phase, then one wave's crests will coincide with another wave's troughs and so will tend to cancel out. The resultant amplitude is A = |A1 − A2|. If A1 = A2 the resultant amplitude will be zero. This is known as destructive interference.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~