# Coherent waves for interference

1. Nov 11, 2013

### ppy

Hi,

Can someone give me an explanation as to why coherent waves are needed for interference. I know coherent waves are when the phases difference between the waves is a constant and the frequency of the waves are constant.

Thanks :)

2. Nov 11, 2013

### Cthugha

Interference works by superposition of fields. If you have two fields at some position, they add up according to their phase. You get a higher total amplitude when they are in phase, you get a smaller total amplitude when they are out of phase and you can get everything in between. If this phase is fixed, this means that the fields always add up or are always reduced. If you have incoherent beams, their relative phase varies over time. The amplitudes sometimes add up and sometimes they are subtracted.

Now it depends on "how fast you look". When you try to capture an interference pattern created by fields with phase varying over time, you will see a mixture of adding up and getting subtracted, if you have a look at the pattern averaged over a timescale which is longer than the timescale on which the phase randomizes. This will sum up to no pattern at all. If you just look at the pattern on a much shorter timescale than the timescale over which the phase randomizes, you will still see the pattern.

If this phase randomizing timescale is long, the fields are usually called mutually coherent. If it is short, they are called incoherent. However, there is no well defined border in between.

3. Nov 12, 2013

### sophiecentaur

The simplest ('perfect') example of interference would be when you have two identical sources of a single frequency of wave. The phase relationship between the two waves, as they arrive at any point, will be constant, so you will get the same resulting peak amplitude for the resultant at all times. This can occur (to within a very close tolerance) with loudspeakers, fed from the same tone source or with antennae, fed from the same transmitter (or from two phase locked transmitters) and will give you a 'perfect' interference pattern. The two sources are highly coherent.
If one transmitter can drift, relatively, in frequency by 1Hz (now they are non-coherent), the phase relationship will be drifting by 360° every second and the interference pattern will change maxes and mins twice every second as the vectors drift relative to each other. You will not measure any pattern if you try to detect it over a period of time.
In any practical case, the two sources will not be exactly in phase (not perfectly coherent) they can be regarded as a mixture of frequencies around a central value. They will have a spread of relative phase over time. If you use light sources, there can be a relatively wide fractional spread of frequencies which will mean that the two interfering beams will have a non-constant phase relationship which will result in the various waves producing minima at slightly different angles (filling in the pattern). The higher the degree of coherence, the more tolerant is the system to the path lengths for the various 'beams' involved. A laser can give light with such high coherence that light falling on a large object will produce a good enough diffraction pattern to give you a hologram. You can also produce acoustic holograms with a source of ultrasound and get a holographic image of an object.

4. Nov 15, 2013

### Claude Bile

Coherent waves are needed because they ensure that the phase relation between two waves being superimposed is fixed.

If the phase relation is not fixed (i.e. random over time), then when we calculate irradiance (by performing a time-average integration of the EM field), the interference term vanishes.

Constant frequency is not required; just correlated (coherent) phase.

Claude.