Three-dimensional rooms yield denser mode distributions at higher frequencies

Evidence

There is no denying the qualitative difference as compared to 1D: 2D and 3D mode densities have a seemingly irregular set of frequencies growing denser with increasing frequency. The density ρ of modes-the number of modes per Hz-goes up with frequency f in a three-dimensional space, as where V is the volume of the room, S is the surface area of the room, and L is the length of the room edges. — Eric J. Heller, Why You Hear What You Hear- An…, 2434

Categorization

• DEFINE: Defines mode density, the count of resonant modes per Hz, and how it scales with dimension.