burke11,
The phenomenon that produces these counterintuitive dips and peaks is called "comb filtering." When a reflected sound bounces around the room, it interferes with other sound waves that are just now leaving the speaker (or other reflections). These reflections are all out-of-phase with one another, and comb-filtering is the result. Some frequencies show peaks, others show nulls, such as yours at 4k.
By using absorption, you reduce the number and intensity of waves bouncing around the room, which reduces comb filtering, which reduces the nulls (and peaks) you are experiencing.
For more on this idea, see this article:
RealTraps - Acoustics Fact & Fiction
Or watch the "Comb Filtering" video, about halfway down our videos page:
RealTraps - Videos
Also, JDG is referring to our ceiling tiles:
RealTraps - Ceiling Tiles