Why would sound reverberate indefinitely in two spatial dimensions? I came across this amazing fact that the sound propagation is distortionless only in odd dimensions, due to Huygens' principle (found in the abstract)[1]. Digging deeper, this webpage by Wolfgang Bangerth has a section on acoustic waves in a cylindrical coordinate system. The last paragraph accompanied with a video gathered my attention:

The lack of silence after the first wave has arrived means that if we were living in a two dimensional world, there would be a reverberation after each sound. People would say something, then shut their mouth, but there would still be coming a sound from their direction. It has been said that it would be very loud in a two dimensional world.

What is the reason behind this eternal reverberation?
 A: This may not be a very satisfactory answer depending on your level of understanding of partial differential equations but...
This is related to the behavior of the Green's function for the wave equation.  This is a solution that represents the field due to a point impulse, a single pulse on-off concentrated at a point in space.  The behavior of the function in 3d is such that for an impulse the signal at a later time is concentrated on a spherical surface.  In 2d the field due to a concentrated impulse is spread out through the entire region contained within the leading edge of the wave.  One could say that this comes from the math, to the extent that this math adequately describes the physics of the system.  Acoustic waves exist in a medium and the "wave equation" is derived by considering small fluctuations about some background movement in the fluid (medium).  For large amplitude sound the wave equation is no longer valid (but then again some might argue that the classic definition of sound becomes invalid).  If the medium has loss in it then this reverb will die.  What is being described is the ideal behavior predicted by the Green's function.  
I am not sure what "distortionless" means in this context.  I think of distortion as being due to interference from rough surfaces etc, that causes rapid, seemingly random, phase fluctuations and that can happen in 3d when boundaries are present.  
I hope this helps a little.  I'd recommend Morse and Feshbach Methods of Theoretical Physics Part I for more on the Green's function.  They describe exactly this behavior in that chapter.      
