These two images were for an acoustic study for Dartmouth College. My task was to diagram ray tracing to show how reflectors can help diffuse sound in a room with four barrel vaults. The first image shows the room as it currently is. The barrel vaults cause heavy focusing in the room. A whisper-gallery effect happens in which the sound energy travels along the arch of the vault without losing much energy. This causes some odd focusing and imaging effects.
The Second image shows how the sound would behave if reflectors were installed with a 6″ camber. The reflectors diffuse the sound over the room and help eliminate the focusing effects while increasing communication within the space.