Sound Power Level

Sound power is the total acoustic energy radiated by a source per unit time, measured in watts. Unlike sound pressure, which depends on distance, room acoustics, and directivity, sound power is an intrinsic property of the source. It enables objective comparison of noise emissions across different sources and measurement environments.

Fundamental Formula

The sound power level (L_W) is defined relative to a reference power of 10⁻¹² watts:

L_W = 10 · log₁₀(W / W_ref) [dB re 10⁻¹² W]

Sound power is determined indirectly by measuring sound pressure levels over a defined measurement surface surrounding the source and integrating:

W = (1 / ρc) ∫_S p²(r) dS

where ρc is the characteristic impedance of air (approximately 413 Pa·s/m at 20°C), and the integral is taken over the measurement surface S enclosing the source.

ISO Standards

Standard	Grade	Environment	Accuracy
ISO 3744	Engineering (Grade 2)	Free field over reflecting plane, or outdoors	± 2–3 dB
ISO 3745	Precision (Grade 1)	Anechoic or hemi-anechoic chamber	± 0.5–1 dB
ISO 3746	Survey (Grade 3)	Any environment with corrections	± 4–5 dB

ISO 3744 — Engineering Grade

The most commonly used standard. Microphones are placed on a hypothetical measurement surface (hemisphere, rectangular parallelepiped, or conformal surface) surrounding the source. The environment must approximate a free field over a reflecting plane. Background noise corrections are applied when the ambient level is within 6–15 dB of the source-on level.

ISO 3745 — Precision Grade

Requires a qualified anechoic or hemi-anechoic room. More microphone positions are used (at least 20 for a full sphere), providing detailed directivity information. This is the reference method for verifying results from other grades.

Measurement Surface Setup

The measurement surface defines the spatial integration domain. Common configurations:

Surface Shape	Typical Use	Minimum Microphones
Hemisphere	Small to medium sources on a floor	10 (ISO 3744), 20 (ISO 3745)
Rectangular Parallelepiped	Large or rectangular machinery	9–12 on each face
Conformal Surface	Source with complex geometry	Adapted to geometry

The measurement distance must be at least twice the largest source dimension and at least 1 meter. Each microphone position represents an area element S_i of the measurement surface, and the sound power is computed as:

L_W = 10 · log₁₀[ (1/S_ref) ∑_i=1^N S_i · 10^L_pi/10 ] + 10 · log₁₀(S/S_ref)

Directivity

The directivity index D_I(θ, φ) describes how the source radiates preferentially in certain directions:

D_I(θ, φ) = L_p(θ, φ) − L_p,avg [dB]

A positive D_I indicates that the source radiates more strongly in that direction than the spatial average. Directivity is essential for predicting noise levels at specific receiver positions and for designing noise barriers and enclosures.

Frequency-Band Sound Power Spectrum

Sound power can be determined per frequency band (octave or one-third octave) to reveal the spectral distribution of radiated energy. The per-band L_W is computed by applying the measurement surface integration to the band-filtered pressure levels. This spectral breakdown guides noise control decisions: identifying which frequency bands dominate the total power output helps prioritize treatment strategies.

Parameters

Parameter	Options	Description
Standard	ISO 3744, ISO 3745, ISO 3746	Measurement grade and procedure.
Surface Shape	Hemisphere, Parallelepiped, Conformal	Geometry of the measurement surface.
Measurement Radius	≥ 1 m	Distance from source center to microphone positions.
Number of Positions	Standard-dependent	Number of microphone locations on the surface.
Frequency Weighting	A, C, Z	Applied to the final sound power level.
Band Analysis	Broadband, Octave, 1/3 Octave	Spectral resolution for frequency-band power.
Background Correction	Auto / Manual / None	Correction for ambient noise contribution.

Practical Tips

Always perform a background noise measurement before and after the source measurement. If the difference is less than 6 dB at any band, the result at that band cannot be reported per ISO 3744.
Verify the measurement environment qualification by checking the deviation from theoretical inverse-square-law decay across the measurement surface.
For comparative testing (e.g., before/after noise treatment), the same measurement setup and microphone positions must be used to ensure valid comparison.
A-weighted sound power (L_WA) is the most commonly cited single-number metric for product noise declarations and labeling regulations.

Sound power level is typically 10–15 dB higher than the sound pressure level measured at 1 m distance from a compact source in free field. Do not confuse L_W with L_p when interpreting noise specifications.