Interference conditions problem We know that two wave sources can interfere if 


*

*two sources have the same frequency

*two sources must have a constant phase difference over time.


But I think that if condition 1 is satisfied, condition 2 is too. So is the second condition unnecessary? There must be some counter-example, isn't there?
 A: When we say two sources have the "same" frequency, there is often a limit on what "same" means. Specifically, we usually recognize coherence as an essential attribute for creating interference.
Let's look at the example of a laser. To create interference, you can split a laser into two beams, then let these beams interfere with each other. With the right setup, you get fringes. But if you add an additional (constant) path to one "leg" of the laser light, you will see that as the total path difference gets bigger, the fringes become less well defined.
In essence, what is happening in that example is that you start to measure the limits of coherence of your laser - at what time/path difference is the phase relationship between the two beams still well-defined? Tiny fluctuations in the frequency eventually build up and cause "decoherence" at sufficiently long path lengths. This mechanism can be used to measure just how much a frequency source fluctuates - the width of the autocorrelation of the signal tells you about the bandwidth.
The key here is that there is no such thing as "monochromatic" light, or a source of "constant" frequency. Every signal made in nature has a degree of incoherence - whether it be Doppler shifting due to thermal motion, or any one of a myriad of other causes. Great care is taken to make some very stable oscillators - the Cesium clock standard is at an error rate of less than a second in 100 million years - but that is still not "constant". So even two Cesium clocks will eventually drift; and oscillators derived from these clock will not guarantee a constant interference pattern.
The way this is usually solved is by making sure that path lengths from the source to the point of interference are kept constant. This way, any phase error in one arm is replicated in the other arm, and the interference pattern is preserved.
A: Most light sources do not emit a constant phase, unlike radar or audio sources.  So while all the light may be of a given wavelength, the random (in time) phase shifts can kill interference.
