Radiation Efficiency⚠ unverified
Physics / Acoustics · Compute an approximate radiation efficiency for a panel
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| f | f | Hz | 1.0 | Excitation frequency |
| fc | fc | Hz | 1.0 | Critical (coincidence) frequency |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | σ | — | Radiation efficiency, dimensionless |
The science & history
Understanding the Parameters
- $f$ — band or pure-tone frequency.
- $f_c$ — coincidence critical frequency of the panel.
- Output — grows as $f^{2}$ below $f_c$; real $\sigma$ saturates and depends on geometry, boundary conditions, and whether $f$ is above coincidence.
Derivation (Approaching a Proof)
Radiated power $W \approx \sigma \rho c S \langle v^{2}\rangle$ defines radiation efficiency $\sigma$. For infinite plates, $\sigma(f)$ has a characteristic rise through $f_c$. Elementary textbook sketches sometimes use $\sigma \propto (f/f_c)^{2}$ well below coincidence — an order-of-magnitude model only.
History
Radiation efficiency is standard in statistical energy analysis (SEA) and building acoustics prediction of structure-borne sound.
Related Concepts: Critical Frequency, Sound Power Level, Transmission Loss
Notes: Registry calculator radiation-efficiency (unverified). Heuristic $(f/f_c)^{2}$ only;
not capped at 1.