Wave interference

Interference of the two signals of the same frequency, emitted through the two adjacent sources at the center. This applet allows wide range of experiments with interference, allowing to set various signal sources

In physics, interference is the addition (superposition) of two or more waves that results in a new wave pattern. Interference usually refers to the interaction of waves that 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. Interference in physics corresponds to what in wireless communications is called multi-path propagation and fading, while the term interference has a different meaning in wireless communications.

The principle of superposition of waves states that the resultant displacement at a point is equal to the vector sum of the displacements of different waves at that point. If a crest of a wave meets a crest of another wave at the same point then the crests interfere constructively and the resultant wave amplitude is increased. If a crest of a wave meets a trough of another wave then they interfere destructively, and the overall amplitude is decreased.

This form of interference can occur whenever a wave can propagate from a source to a destination by two or more paths of different length. Two or more sources can only be used to produce interference when there is a fixed phase relation between them, but in this case the interference generated is the same as with a single source; see Huygens' principle.

Interference patterns

For two coherent sources, the spatial separation between sources is half the wavelength times the number of nodal lines.

Light from any source can be used to obtain interference patterns, for example, Newton's rings can be produced with sunlight. However, in general white light is less suited for producing clear interference patterns, as it is a mix of a full spectrum of colours, that each have different spacing of the interference fringes. Sodium light is close to monochromatic and is thus more suitable for producing interference patterns. The most suitable is laser light because it is almost perfectly monochromatic.

Constructive and destructive interference

Consider two waves that are in phase, with the same 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 π radians, or 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. In the applet on the left, destructive interference forms clearly visible "rays", where the surface is largely still. If these were the two radio stations, radio receiving would not be possible inside these rays.

When two sinusoidal 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 an amplitude between 0 and 2A depending on whether the two waves are in phase or out of phase.

Acknowledgements

This web page reuses material from Wikipedia page http://en.wikipedia.org/wiki/Wave_interference under the rights of CC-BY-SA license. As a result, the content of this page is and will stay available under the rights of this license regardless of restrictions that apply to other pages of this website.

Also, we reuse code of the interference applet by Paul Falstad (required attribution)