Mean Free Path
where is the total volume of the room, and is total surface area enclosing the room.
Regarding each delay line as a mean-free-path delay, the mean free path length, in samples, is the average delay-line length:
where = sound speed and = sampling period.
This is only a lower bound because many reflections are diffuse in real rooms, especially at high frequencies (one plane-wave reflection scatters in many directions)
Mode Density Requirement
FDN order = sum of delay lengths: