Sound Intensity Level⚠ unverified
Physics / Acoustics · Compute the sound intensity level in decibels
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| I | I | W/m**2 | 1.0 | Sound intensity |
| I_ref | Iref | W/m**2 | 1e-12 | Reference sound intensity, in watts per square metre (W/m**2). Default is 1e-12 |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | LI | dB | Sound intensity level, in decibels (dB). Returns negative infinity when ``I`` is not positive |
The science & history
Understanding the Parameters
- $I$ — from measurement or $p^{2}/Z$ (Sound Intensity).
- $I_{\mathrm{ref}}$ — ISO reference; keep consistent with the medium/standard you cite.
- $L_I$ — numerically close to $L_p$ for progressive plane waves in air when references match.
Derivation (Approaching a Proof)
By definition of the decibel for a power-like ratio:
$$L_I = 10\log_{10}\frac{I}{I_{\mathrm{ref}}}.$$
With $I \propto p^{2}$, $L_I = L_p$ when $I_{\mathrm{ref}} = p_{\mathrm{ref}}^{2}/Z_0$ for the same medium — the usual air pairing of $20\,\mu\mathrm{Pa}$ and $10^{-12}$ W/m².
History
Intensity level parallels SPL for energy-based descriptors and sound-power estimation from intensity scans.
Related Concepts: Sound Intensity, Sound Pressure Level, Sound Power Level, SNR to Decibels
Notes: Registry calculator sound-intensity-level (unverified). Uses $\log_{10}$ (registry may
write log10).