Sound Pressure Level✓ verified
Physics / Acoustics · Sound pressure level in decibels relative to the 20 uPa reference
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| p_rms | p | Pa | 1.0 | RMS sound pressure |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| spl | Lp | dB | Sound pressure level |
The science & history
Understanding the Parameters
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$p$ — RMS pressure of the sound wave (not peak unless converted). Atmospheric pressure is ~101 kPa; audible sounds are tiny fractions of a pascal.
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$p_{\mathrm{ref}}$ — fixed at $2\times 10^{-5}$ Pa for airborne SPL in the standard definition; the registry equation shows $p_{\mathrm{ref}}$ but may not expose it as an input.
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$L_p$ — 0 dB ≈ threshold of hearing; 60 dB conversation; 120 dB near pain.
Derivation (Approaching a Proof)
Acoustic intensity $I \propto p_{\mathrm{rms}}^{2}$. Level in dB for a power-like ratio is $10\log_{10}(I/I_{\mathrm{ref}})$. Substituting $I/I_{\mathrm{ref}} = (p/p_{\mathrm{ref}})^{2}$ gives
$$L_p = 10\log_{10}\left(\frac{p}{p_{\mathrm{ref}}}\right)^{2} = 20\log_{10}\frac{p}{p_{\mathrm{ref}}}.$$
Same 20-vs-10 logic as THD to Decibels vs SNR to Decibels.
History
The decibel SPL scale was standardised for telephony and occupational noise; $20\,\mu\mathrm{Pa}$ is the ISO reference for air.
Related Concepts: Sound Intensity Level, Sound Power Level, Sound Intensity, A Weighted Level, SNR to Decibels
Notes: Registry calculator sound-pressure-level (unverified). Confirm $p_{\mathrm{ref}}$ is the
air standard if not user-set.