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A space with this condition is called a diffuse sound field.
With the ability to simulate realistic modeling boundary conditions by combining dynamic, kinematic and acoustic constraints, as well as physical excitations like diffuse sound field and turbulent boundary layer, you can obtain accurate representation of the acoustic performance of your designs.
What is interesting is that, in a totally diffuse sound field, the center time index would have a perfect correlation with the sound reverberation time of a space.
Sound Source Room acoustic measurements require a sound source with a diffuse sound field, which means that the sound energy has to be distributed uniformly.
In Europe, the Bonn Beethoven Hall's acoustical design intentionally aimed to create a diffuse sound field by placing sound diffusing structures on all of the walls and the ceiling, but I for one have not heard accolades about this hall.
This appears to be the origin of use of the word "diffuse" in the context of acoustics. Sabine defined "diffuse sound field" as a room where (either in a transient state or in a state of equilibrium) the acoustic energy is uniform throughout the room and where there is an equally probable propagation of sound from all directions at all points in the room.
As for the shape of the room, irregular shaped rooms with slanted walls and ceiling for achieving diffuse sound field condition are common in Japan, but the cuboid reverberation rooms with an appropriate ratio of room dimension with some improvement have become more common.
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