Sound Power Level⚠ unverified
Physics / Acoustics · Compute the sound power level in decibels
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| W | W | W | 1.0 | Sound power |
| W_ref | Wref | W | 1e-12 | Reference sound power, in watts (W). Default is 1e-12 |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | LW | dB | Sound power level, in decibels (dB). Returns negative infinity when ``W`` is not positive |
The science & history
Understanding the Parameters
- $W$ — total radiated acoustic watts (often ≪ mechanical input power).
- $W_{\mathrm{ref}}$ — ISO reference for air-borne $L_W$.
- $L_W$ — used with distance and directivity to predict $L_p$ in free field: $L_p \approx L_W + 10\log_{10}(Q/(4\pi r^{2}))$ (plus constants for the chosen reference set).
Derivation (Approaching a Proof)
Again a power ratio in decibels:
$$L_W = 10\log_{10}\frac{W}{W_{\mathrm{ref}}}.$$
Integrating intensity over a closed surface: $W = \oint \mathbf{I}\cdot d\mathbf{A}$.
History
Sound power level is the manufacturer rating for machinery noise; EU/outdoor equipment directives quote $L_W$.
Related Concepts: Sound Intensity Level, Sound Pressure Level, Sound Intensity, Radiation Efficiency
Notes: Registry calculator sound-power-level (unverified).