Finding Constructive Interference

[Patdon10]

Homework Statement

A college student is at a concert and really wants to hear the music, so she sits between two in-phase loudspeakers, which point toward each other and are 53.2 m apart. The speakers emit sound at a frequency of 459 Hz. At the midpoint between the speakers, there will be constructive interference, and the music will be at its loudest. At what distance closest to the midpoint could she also sit to experience the loudest sound?

Homework Equations

The Attempt at a Solution

My book is absolutely useless in this problem. It really gives no useful information in how to solve this problem. Can anyone point me in the right direction?

I learn through examples, and I'm absolutely willing to try. This problem is from my last homework assignment (meaning it won't help my grade), I'd just like to learn how to do it.

 

[ideasrule]

Constructive interference happens when the path lengths to the two sources differ by an integer multiple of a wavelength. That way, the crest from one wave reaches the listener at the same time as the crest from the other, and ditto for the trough. So, which other places between the two speakers have path lengths that differ by an integer multiple of 53.2 m?