Frequency of first intensity maximum for loudspeakers

[vaizard]

Homework Statement

Two loudspeakers are set up 4.0 meters apart and are driven in phase by the same amplifier. The listener is located a sufficient distance away so the angle to the listener is approximately the same at each speaker as indicated in the drawing. The speed of sound is 344 m/s. What frequency would the speakers need to emit if the first intensity maximum from the central maximum occurs at an angle of 30° from the perpendicular to each speaker?
http://omploader.org/vMTBsaw/phys_diagram1.png

Homework Equations

$$v=\lambda \cdot f$$
There is also $$A = 2 A_0 cos(\frac{\phi}{2})$$ in the solution to the problem but I don't understand where this equation even came from. It's not in my book or anything.

The Attempt at a Solution

Well, I know I'm looking for f, the frequency. So I did $$f = \frac{v_{\mbox{sound}}}{\lambda}$$ but that's about it. Now the actual solution uses $$A=2A_0 cos(\frac{\phi}{2})$$ and $$\phi = k \Delta x$$. I would like to understand where these equations came from. Are they universal for this type of problem, or were they somehow derived from the given information?

http://omploader.org/vMTBsbQ/phys_diagram2.png

 

[Carid]

Surely the first max will occur when the path length from one speaker is a single wavelength longer than to the path length to the other.
The path difference shown here is 4*sin30° = 2metres
So 344m/sec = 2m * frequency
Frequency = 172 Hertz.