Why must interference be observed with coherent sources? (phase difference) I get that they must have the same frequency, but why must they have constant phase difference?
 A: In theory, all waves interfere with each other, but the case where they are the same frequency is where some of the most interesting interference takes place.  If the sources have the same frequency, then there will be points in space where the path length differences between the point and the two sources and their phase difference line up to create destructive cancelation (180 degrees out of phase).  At these points, we see no energy, no matter what time we observe it.  Everywhere else we may observe no energy some of the time and lots of energy at other times, but at these "nulls" we never see any energy at all.  If these are photons interfering, the lines are "dark."
You can have a non-constant phase difference between the two sources.  The result is that the nulls will appear in different places because the correct path lengths to cause destructive interference are different.  As you adjust the phase difference, the nulls will appear to "move."
If you change the phase difference too rapidly, the nulls will move so quickly that it will start to be difficult to detect them.  They will cease to be "special" and we'll start ignoring them.
A: When you have two sound source with two slightly different frequencies $f_1$ and $f_2$ you will hear a variation in the loudness of the sound with a frequency $|f_1-f_2|$.
These are called beats.
You can think of this as two sources whose waves overlap and form a moving interference pattern.
In other words instead of at one position only hearing a maximum loudness if the frequencies of the sources were exactly the same, the positions where there is maximum loudness move.  
You can think of the waves from the two sources as continuously changing in phase relative to one another.
So if for sound wave if the two frequencies are $256\,\rm Hz$ and $257\,\rm Hz$ then the beat frequency will be $1\, \rm Hz$ which is easily detectable.  
If the frequencies if the two sound waves were the same but in some way you randomly changed the phase between them then the interference pattern would move with every change of phase.
If the change in phase occurred very often per second then you would not be able to discern  the changes in intensity.
Now for light the problem is that the frequencies are of order of magnitude $5\times10^{14}\,\rm Hz$.
To get a pattern which is observable to the eye the pattern cannot change in less than $\frac{1}{30}\,\rm s$ which corresponds to a "beat" frequency of $30\, \rm Hz$, the two light sources have to differ in frequency by less than  $30\, \rm Hz$.  
Two sources which produce waves that overlap will produce an interference pattern.
The question is, will the interference pattern be in roughly the same place over the period of time that is needed to observe it?
