Sound Pressure Level (Lp): Definition, Measurement, and Applications

Acoustic pressure vs. sound pressure level

• Acoustic pressure p(t) is a physical quantity in pascal (Pa).
• SPL L_p is a level, i.e., a logarithmic ratio that compresses dynamic range and aligns with loudness trends in human perception.

Frequency and time dependence

Real sound varies over frequency and time. Two important constructs support comparability:

• Frequency weighting (often A-weighting, denoted L_A or L_Aeq) approximates the ear’s sensitivity at moderate levels, emphasizing mid-frequencies and attenuating extremes. C-weighting and Z-weighting (flat) are also used.
• Time weighting (Fast, Slow, Impulse) defines detector dynamics for fluctuating signals. Modern measurements often report equivalent continuous SPL, L_eq,T, defined by:

L_eq,T = 10 log10[(1/T) ∫_0^T (p(t)^2 / p_0^2) dt] dB

Field and geometry effects

In the far field of a source in free space, SPL follows the inverse-square law:

E_v = I / r^2,
L_p ≈ L_w - 10 log10(4π r^2 Z_0)  (plane-wave approximation)

with Z₀ = ρ₀ c the characteristic impedance of air. In rooms, reflections, standing waves, and diffuse-field conditions alter this relationship; corrections or averaging strategies are required.

Microphones and front-end

Precision measurement microphones (free-field or diffuse-field types) convert pressure to voltage. Key specifications include sensitivity, frequency response, dynamic range, and environmental stability. Windscreens mitigate turbulence; preamplifiers and low-noise conditioning preserve signal integrity.

Calibration

• Primary calibration uses pistonphones or couplers that apply a known pressure at a known frequency.
• Electrostatic actuators and reciprocity methods support wideband or high-accuracy calibrations.

Calibration certificates should state reference conditions (temperature, pressure, humidity), uncertainties, and traceability chain.

Uncertainty contributors

Dominant terms include microphone sensitivity, frequency weighting tolerances, cosine response (if incidence is oblique), environmental effects (temperature, humidity, barometric pressure), cable/connector thermoelectric offsets, and background noise. Reporting should include expanded uncertainty and test conditions.

Environmental acoustics

Community noise assessments, airport contours, and transportation projects rely on A-weighted L_eq,T, day-evening-night metrics, and percentile levels L₁₀, L₅₀, L₉₀. Compliance assessments hinge on robust sampling strategies and meteorological screening.

Building and architectural acoustics

SPL measurements evaluate room modes, background noise criteria (e.g., NC/NR/RC), and isolation performance via source-receiver configurations. Results guide HVAC design, façade upgrades, and room treatments.

Product testing and safety

Appliance, tool, and machinery specifications include emission SPL at defined operator positions. Hearing-conservation programs evaluate peak SPL and time-weighted L_Aeq to assess exposure risk and define hearing protection.

Audio engineering and electroacoustics

Loudspeaker tuning, room equalization, and PA system alignment rely on spatially averaged SPL and transfer-function analysis, integrating SPL data with phase and coherence diagnostics.