# Superposition of waves

1. Dec 7, 2008

### leopard

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

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

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

Bottom figure:

$$P_{1}=P_{2}=P_{3} = 10W$$, same problem.

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

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.

2. Dec 8, 2008

### turin

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