Modal density scales with spatial dimension, from flat in 1D to squared in 3D.

Evidence

The density of modes increases rapidly as a function of frequency, and is proportional to the square of the frequency. Note that the density of modal frequencies df is approximately constant for one-dimensional acoustic systems, such as strings (Figure 2.13) and tubes (Figure 2.12), directly proportional to the frequency (df ∝f) for two-dimensional acoustic systems, such as a membrane (Figure 2.15), and proportional to the square of the frequency (df ∝f 2) for three-dimensional acoustic systems, such as rooms. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 294

Categorization

• DEFINE: Explains the concept of modal density and how it scales with the dimensionality of the acoustic system.