Circle Side Effects!

In the last post I talked about "Circle Side Effects" so I will explain what I meant by that. 

Have you ever been to the room where they keep The U.S Constitution in D.C? You might have noticed this room is circular and that you can hear conversations occurring on the opposite side of  the room, almost perfectly! This is "whisper effect" and circles are prone to this because of the focused reflections that occur in a circle. Take this picture:

The yellow lines represent the reflection patterns of a sound source in this space over a given time (2 seconds, and calculating 3rd order reflections). The "starburst" looking pattern at the top of the circle is the source, this is where the sound is coming from. Do you notice anything odd about these reflections? 

See the "inner circle" that is created by the concentration of yellow lines near the bottom of the image? That means that this area is receiving more reflections than say the middle of the circle...this essentially is what leads to whisper effect!

For some contrast let's look at a square shape:

See the difference? The concentration of reflections is much lighter, so whisper effect doesn't occur.

Obviously the whisper effect could be very problematic for a courtroom so this is the main problem that I must account for, handling the reflections of the circle.