Can any type of wave produce an interference pattern from two sources? Can any type of wave produce an interference pattern similar to the one in a double slit experiment? So for example, could a radio wave create an interference pattern through the airwaves?
 A: The only requirement for wave interference is the principle of superposition:
$$ W(x,t) = W_1(x,t) + W_2(x,t) $$
That is, the total wave amplitude is simply the sum of the amplitudes of the other interfering waves.  This condition, along with the condition that the two sources start in phase, are the only requirements needed to describe an interference pattern such as from a double-slit experiment. 
Radio waves obey they law of superposition, and so you could perform a double-slit experiment with them. 
A: The only necessary condition for interference is that the sources must be coherent (constant phase difference and same wavelength). It is impossible for two independent sources to be perfectly coherent as there will always be random variations in the emission of the photons. Hence it is impossible to produce a sustained interference pattern with two sources.
A: Yes any two wave can interfere having same nature like we can  do double slit experiment through the sound wave, for two wave to show interference pattern, phase difference should be constant what I am saying is this.) 
Consider say two electromagnetic wave, whose phase difference changes with time. 
$$E_1=E_0sin(wt_1-kx)$$,and $$E_2=2E_0sin(wt_2-kx)$$,
And for phase difference. 
$(wt_1-kx) - (wt_2-kx) =H$ (where H is phase difference). 
it is very difficult to know how they wave interfere at that particular instant.beacuse of their phase changes with time.  So conclusion is 
two similar wave (wave have same kind of nature)  can interfere to produce resulting wave, where $A$ will be the resultant amplitude, two sources should be coherent. 
