With sufficient dissipation, closed and open resonant systems become spectrally equivalent
Evidence
If the wedge is closed off with an outer wall a great distance out, the echoes cease for a while but return after bouncing off the wall, eventually giving sharp resonances after many such trips. If the wedge is closed off but the waves damp out due to propagation losses of any sort, they may fail to make the round-trip off the outer wall (if they even make it that far). Thus, with enough dissipation, there is little difference between an open wedge and a closed one; this (and the sculpting principle and average power theorem) tells us that the smoothed high-resolution spectrum of a high-Q closed wedge is just the spectrum of an open wedge. β Eric J. Heller, Why You Hear What You Hear- Anβ¦, 1146
Categorization
- DEFINE: This is the core statement of the average power / dissipation equivalence principle: dissipation erases the distinction between open and closed geometries.