Two- and three-dimensional systems show rapidly rising modal density

Evidence

A violin, a soundboard, or a room differ qualitatively from pseudo-one-dimensional systems like strings and narrow air columns. One-dimensional systems support waves that can be specified simply as amplitude or pressure along a one-dimensional path. Although they can have narrow or broad resonances, they don’t have a rapidly rising density of modes with increasing frequency, unlike two-or three-dimensional systems that can find many ways to vibrate having almost the same frequency. This is especially true at higher frequencies. The density of modes (how many are there in a given frequency interval?) has important implications for how two-and three-dimensional objects accept and transmit sound. — Eric J. Heller, Why You Hear What You Hear- An…, 1123

Categorization

• DEFINE: Defines ‘density of modes’ and contrasts 1-D with 2-D/3-D vibrators.