# Wave interference on beachfront

## Homework Statement

While walking along the shore at your beachfront home, you notice that there are two narrow gaps in the breakwater, the wall that protects the shore from the waves. These gaps are 9.0 m apart and the breakwater is 12.0 m from the shore and parallel to it. You go to the shore directly opposite the mmidpoint between the gaps. As you walk along the shore, the first point where no waves reach you is 1.7 m from your starting point. Out beyond the breakwater you observe that there are ten wave crests in 18 s. How far apart are the wave crests? (Note: The distance of the person from the gaps is not large compared to the separation of the gaps, so the path length difference is not accurately give by $$\Delta l=dsin\theta$$)

## Homework Equations

$$\Delta l=dsin\theta$$ (disregarded)
$$tan\theta= y/L$$

## The Attempt at a Solution

I tried solving this by directly finding the path lengths r1 and r2 using geometry and similar triangles, but I don't think this would work since the subtraction would rely on them being parallel. I did:

http://img683.imageshack.us/img683/2263/wavesl.jpg [Broken]

Found r1 using pyth. Theorem, found r2 using similar triangles and pyth. theorem. Subtracted the values and plugged the result into the phase difference equation. The phase difference is pi/2 since the spot on the shore is destructive interference.

Like I said I don't think this is correct, what should should I do?

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