Sound Intensity⚠ unverified
Physics / Acoustics · Compute sound intensity from pressure and acoustic impedance
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| p_rms | prms | Pa | 1.0 | Root-mean-square sound pressure |
| Z | Z | Pa*s/m | 1.0 | Specific acoustic impedance |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | I | W/m**2 | Sound intensity, in watts per square metre (W/m**2). Returns 0.0 when ``Z`` is not positive |
The science & history
Understanding the Parameters
- $p_{\mathrm{rms}}$ — same pressure used in SPL.
- $Z$ — air ≈ 413 Pa·s/m at STP; water much larger.
- $I$ — reference intensity for SIL is $10^{-12}$ W/m² (Sound Intensity Level).
Derivation (Approaching a Proof)
Instantaneous intensity $I(t) = p(t)\,u(t)$. For a plane progressive wave $p = Z u$, so $I_{\mathrm{avg}} = p_{\mathrm{rms}}^{2}/Z$ (mean of $p^{2}/Z$). Also $I = p_{\mathrm{rms}} u_{\mathrm{rms}}$ when in phase.
History
Intensity links measurable pressure to energy transport; sound-intensity probes map energy flow in complex fields.
Related Concepts: Acoustic Impedance, Sound Intensity Level, Sound Pressure Level, Sound Power Level
Notes: Registry calculator sound-intensity (unverified). Plane progressive wave relation.