Sound Pressure Level (dB SPL) Formula
Quantifies audible acoustic sound pressure level on a logarithmic decibel (dB) scale referenced to the human threshold of hearing at 1,000 Hz (20 µPa).
\[ L_p = 20 \log_{10}\left( \frac{p_{rms}}{p_0} \right) \quad \text{where } p_0 = 20 \times 10^{-6} \text{ Pa} = 20 \ \mu\text{Pa} \]
Plain Text Formula:
L_p = 20 * log10(p_rms / p0) where p0 = 20 microPascals
📐 Variable Definitions & Parameters
| Symbol | Variable Name | Standard Unit | Physical Definition |
|---|---|---|---|
| \[ L_p \] | Sound Pressure Level | dB SPL | Logarithmic sound pressure magnitude |
| \[ p_{rms} \] | RMS Sound Pressure | Pascals (Pa) | Root-mean-square acoustic pressure fluctuation |
| \[ p_0 \] | Reference Sound Pressure | 20 µPa | Standard auditory threshold reference (2×10⁻⁵ Pa) |
💡 Worked Engineering Example
Problem Statement:
Calculate the dB SPL of a rock concert emitting an acoustic RMS pressure of 2.0 Pa.
Step-by-Step Solution:
- Pressure ratio = 2.0 / (20e-6) = 100,000
- log10(100,000) = 5.0
- L_p = 20 * 5.0 = 100 dB SPL
🎯 Result: Sound pressure level is 100 dB SPL (threshold for required hearing protection).