#### Mode Density Requirement

A guide for the *sum* of the delay-line lengths is the desired
*mode density*. The sum of delay-line lengths in a lossless
FDN is simply the *order* of the system :

Since the order of a system equals the number of poles, we have that is the number of poles on the unit circle in the lossless prototype. If the modes were uniformly distributed, the mode density would be modes per Hz. Schroeder [417] suggests that, for a reverberation time of 1 second, a mode density of 0.15 modes per Hz is adequate. Since the mode widths are inversely proportional to reverberation time, the mode density for a reverberation time of 2 seconds should be 0.3 modes per Hz, etc. In summary, for a sufficient mode density in the frequency domain, Schroeder's formula is

**Next Section:**

Prime Power Delay-Line Lengths

**Previous Section:**

Mean Free Path