Calculating Intensity Variation in Superposition of Waves

[leopard]

Figure on top:
[tex]P_{1}= (1/16)W, P_{2}=1W, P_{3}= 16W[/tex], and I want to calculate how the intensity varies with [tex]\theta[/tex]

[tex]y(r,t) = y_{2}(r,t)[1 + 4e^{i(\phi_{3} - \phi_{2} + kdsin \theta} + \frac{1}{4} e^{i(\phi_{1} - \phi_{2} - kd sin \theta)}][/tex]

I understand how to proceed here, I just want to know how to determine whether it's + or - in front of [tex]\phi[/tex]s and [tex]kdsin \theta[/tex]


Bottom figure:

[tex]P_{1}=P_{2}=P_{3} = 10W[/tex], same problem.

[tex]y(r,t)=y_{1}(r,t)[1 + e^{i(\phi_{2} - \phi_{1} + kd cos \theta)} + e^{i(\phi_{3} - \phi_{1} + kd sin \theta)}][/tex]

Is it just me, or is there an incoherence here, as how to determine the signs? Both are from exam solution manuals at my university, so it should be correct.

 

[turin]

I am having a hard to following the problem setup. Is this some sort of phased array? What is y2?