Interference and wave nature of light

[lovelyrwwr]

Two in-phase sources of waves are separated by a distance of 4.00 m. These sources produce identical waves that have a wavelength of 5.00 m. On the line between them, there are two places at which the same type of interference occurs. Where are the places located?



I already know the answers from this website http://lev.ccny.cuny.edu/~hmakse/TEACHING/204soln27.pdf problem 3. However I cannot for the life of me understand the solution. I especially don't understand why d1 + d2 has to be less than 4. I have spent an hour on this problem and re-reading the explanation and my textbook. But it just doesn't click.

 

[haruspex]

I followed that link, but unfortunately some of the pages appear blank for me, including the one with the relevant solution. Are d1 and d2 the distances from a particular source? If so, let F1, f2 be the distances from the other source. You know d1 + d2 + f1 +f2 = 8m, so either d1 + d2 <= 4m or f1+f2 <= 4m. So choose as reference the source which is nearer on average.

 

[lovelyrwwr]

Here is the solution. I think I am having trouble envisioning the scenario :/

 

[haruspex]

I don't like the wording of the question. Interference will occur everywhere along the line. It ought to specify totally constructive or totally destructive.
I agree the d1+d2=4m argument is a bit glib. By symmetry, if one point is d1 from one source then there must be another such point d1 from the other source. Assuming there are exactly two such points then you can conclude d1+d2=4m.