Sound Power

Standards: ISO 3740 ISO 4871Key references: Beranek & Mellow 2012

Sound pressure depends on where you stand and on the room you stand in; sound power does not. The sound power level $L_{W}$ is the total acoustic energy per second a source radiates, referenced to $P_{0} = 1 pW$ , and it is the device-independent emission descriptor that goes on a datasheet, feeds a room prediction (EN 12354) or is checked against a noise-emission limit. phonometry implements six standardised routes to it, split across four method guides: an enveloping pressure surface in the field (ISO 3744/3746) and the precision grade in an anechoic room (ISO 3745), covered in Sound Power by Pressure Methods; the diffuse field of a reverberation room (ISO 3741), covered in Sound Power in the Reverberation Room; intensity scanning over a surface (ISO 9614-2), with its precision counterpart (ISO 9614-3), covered in Sound Power by Intensity Scanning; and the surface velocity of the machine’s own casing (ISO/TS 7849-1 and -2), the one route that needs no acoustic measurement at all, covered in Sound power from surface vibration. This page is the front door: how to choose among them, what the accuracy grades actually promise, and how a measured $L_{W}$ becomes the ISO 4871 noise-emission declaration a datasheet prints.

Download the animation (WebM)

Choosing a method

All deliver the same quantity, a per-band $L_{W}$ and an A-weighted total $L_{W A}$ , but under different environments, accuracy grades and practical constraints.

Method	Standard	Measured quantity	Environment	Accuracy grade	Use when
Enveloping surface	ISO 3744 (engineering) / ISO 3746 (survey)	Sound pressure on a hemisphere or box	Essentially free field over one or more reflecting planes	Grade 2 ( $σ_{R 0} \approx 1.5 dB$ ) / grade 3 ( $\approx 3.0 dB$ )	In situ or a large room; no special test facility available
Reverberation room	ISO 3741	Sound pressure in the diffuse field	Qualified hard-walled reverberation room	Grade 1 (precision)	Highest accuracy for steady, broadband sources in a lab
Intensity scanning	ISO 9614-2	Normal sound intensity scanned over a surface	Almost any, tolerant of steady extraneous noise	Grade 2 / 3 (from per-band field indicators)	On-site with background noise, or one machine among many
Anechoic room	ISO 3745	Sound pressure on a fixed microphone array	Qualified anechoic or hemi-anechoic room	Grade 1 (precision)	Reference-grade emission in a free-field laboratory
Precision intensity scanning	ISO 9614-3	Scanned normal intensity, tighter criteria	Almost any, tolerant of steady extraneous noise	Grade 1 (precision)	Precision on-site, with the ISO 9614-3 field-indicator checks
Surface vibration	ISO/TS 7849-1 (survey) / -2 (engineering)	Surface-averaged velocity level and a radiation factor	Any; no acoustic measurement	Upper limit ( $ε = 1$ ) / engineering	The machine cannot be quietened, enclosed or approached with a microphone

The pressure methods correct the surface level for the room ( $K_{2}$ ) and for background noise ( $K_{1}$ ); the reverberation method needs a qualified room but reaches precision grade; intensity rejects steady background energy at the cost of a two-microphone probe and a per-band validity check; the surface-velocity route abandons the microphone altogether and pays for it with a radiation factor. Each method guide walks its routes in turn.

Two members of the ISO 3740 family are missing from that table on purpose. ISO 3743-1 and ISO 3743-2 reach engineering grade on small movable sources in a hard-walled or a specially reverberant test room — the route most appliance noise test codes call for — and ISO 3747 determines the sound power of a large fixed machine in situ by comparison against a calibrated reference sound source in a reverberant field. Neither is implemented here. In practice: for a small appliance, ISO 3744 over a hemisphere in the same room is usually available at the same grade; for the in-situ comparison case, the comparison formula on the ISO 3741 page is the same algebra, applied to a qualified room instead of an arbitrary one.

The six sound power routes in two rows of three, each cell carrying the same five attributes. Top row: the ISO 3744/3746 enveloping pressure surface over a reflecting plane, the ISO 3745 fixed array in a wedge-lined anechoic room, and the ISO 3741 diffuse field of a reverberation room. Bottom row: the ISO 9614-2 serpentine intensity scan, the tighter ISO 9614-3 precision scan, and the ISO/TS 7849 accelerometer grid on a radiating casing with no microphone at all

All six deliver the same quantity, and the last one gets there without a microphone. The claim that they agree is checkable, and worth checking once: the block below drives one synthetic source through three of the routes and compares their spectra. It is not a reproduction of the diagram above — a setup diagram has no matplotlib equivalent — but a cross-check you can run.

Show three routes computed on one source

import matplotlib.pyplot as plt
import numpy as np
from phonometry import emission

# One steady source (octave-band LW below) determined by three routes.
freqs = np.array([125.0, 250.0, 500.0, 1000.0, 2000.0, 4000.0])
lw_true = np.array([85.0, 88.0, 90.0, 89.0, 86.0, 82.0])

# ISO 3744: SPL at 10 positions on a hemisphere, r = 2 m (10 lg(S/S0) = 14 dB).
pres = emission.sound_power_pressure(np.tile(lw_true - 14.0, (10, 1)),
                                     "hemisphere", radius=2.0,
                                     frequencies=freqs)
# ISO 9614-2: uniform normal intensity scanned over six 0.5 m2 segments.
i_n = np.tile(10.0 ** (lw_true / 10.0) * 1e-12 / 3.0, (6, 1))
inten = emission.sound_power_intensity(i_n, np.full(6, 0.5),
                                       frequencies=freqs, band_type="octave")
# ISO 3741: comparison against a reference source of known LW = 84 dB per band.
comp = emission.sound_power_comparison(lw_true - 20.0, np.full(6, 64.0),
                                       np.full(6, 84.0), frequencies=freqs)

fig, ax = plt.subplots()
for res, style, ms, label in ((pres, "-o", 11, "pressure (ISO 3744)"),
                              (inten, "--s", 8, "intensity (ISO 9614-2)"),
                              (comp, ":^", 5, "reference source (ISO 3741)")):
    ax.semilogx(freqs, res.sound_power_level, style, markersize=ms,
                label=f"{label}: LWA = {res.sound_power_level_a:.1f} dB")
ax.set(xlabel="Frequency [Hz]", ylabel="Sound power level LW [dB]")
ax.legend()
plt.show()

Before the method: the operating and mounting conditions

Choosing a route is the second decision. The first is what, exactly, is being measured — and for most machine families it has already been made for you. A noise test code is the type C standard for one family of machines: it fixes the basic determination standard, the microphone array, the mounting and the operating mode, and it overrides the general specifications of ISO 3744 or ISO 3741 wherever the two disagree. The same installation, mounting and operating conditions must then be used for the sound power level and for the emission sound pressure level that stands beside it in a declaration, or the two numbers describe two different machines.

Two rules from ISO 3744 clause 6 decide whether a determination is repeatable at all. Auxiliary equipment shall be outside the test environment if it can be; what cannot be removed or adequately quietened is counted as part of the source and the reference box grows to enclose it. And the mounting shall be the typical one, used or simulated — resilient mounts only if the machine is resiliently mounted in the field, because a small machine that is a poor low-frequency radiator on its own becomes a good one through a large panel it is bolted to.

That is also where $σ_{omc}$ comes from. It is not a table lookup: it is estimated from repeated determinations on the same source at the same location, by the same operators, with the same instruments and positions, readjusting the mounting and re-establishing the operating conditions before each one. ISO 3744 Annex H notes 0,5 dB for a well-defined installation, and much larger values where material flow or process variability dominates.

A decision path

The table compresses into a short sequence of questions (ISO 3740 dedicates its Table 3 and Annex D to exactly this decision). Work through them in order; the first match names the standard.

What is the number for? A datasheet declaration or a limit check normally asks for engineering grade (grade 2, the preferred grade for noise declarations); a reference source, a product ranking or a dispute calls for precision (grade 1); a first walk-through of a noisy plant tolerates survey grade (grade 3). Grade 1 exists only in a qualified laboratory room (ISO 3741, ISO 3745) or via the precision intensity methods (ISO 9614-1 at discrete points, ISO 9614-3 by scanning), of which phonometry implements the scanning form only: ISO 9614-1’s own discrete-point power summation is not provided, though its field indicators are (see Sound Intensity).
Can the source travel to a laboratory? ISO 3741 wants the source small next to the room (volume no more than about 2 % of the room volume) and its noise steady; ISO 3745 wants it inside a qualified anechoic or hemi-anechoic room with a characteristic dimension below half the measurement radius, and it is the route that also yields directivity. A machine bolted to its foundation rules both out and leaves the in-situ methods.
How quiet and how dry is the site? ISO 3744 needs the background at least 6 dB below the source (preferably more than 15 dB) and $K_{2} \leq 4 dB$ . If only a 3 dB margin or $K_{2} \leq 7 dB$ can be met, the same microphones and formulae degrade gracefully to ISO 3746 at survey grade.
Is the background the problem? When neighbouring machines cannot be switched off, or the margin is outright negative, the pressure methods are out. Intensity scanning (ISO 9614-2, or ISO 9614-3 for grade 1) tolerates steady extraneous noise even some 10 dB above the source, because only the net energy flux through the surface counts; the per-band field indicators then decide the grade actually achieved.
Can you put a microphone there at all? A machine that cannot be stopped, an environment that destroys a capsule, an enclosure with no room for a surface: when no acoustic measurement is possible, the surface-velocity route estimates the same quantity from accelerometers on the casing (ISO/TS 7849-1 and -2). It answers a subtly different question — it characterises what the structure radiates, and stays blind to sound escaping through openings, intakes and gaps — and it costs a radiation factor you must either assume (Part 1, an upper limit) or measure once (Part 2).
How repeatable is the machine itself? None of the above bounds $σ_{omc}$ , and on a process machine it can outrank the whole grade choice: a grade-1 facility around a source whose own operating conditions scatter by 2 dB buys a $σ_{tot}$ no better than grade 2. Estimate it before paying for the room.

What the accuracy grades mean

The grade is a claim about reproducibility: $σ_{R 0}$ is the standard deviation you would see if different laboratories measured the same source, each following the standard correctly. Typical A-weighted values are $σ_{R 0} \approx 0.5 dB$ for grade 1 (ISO 3741), 1.5 dB for grade 2 (ISO 3744, ISO 9614-2) and 3 dB or more for grade 3 (larger still when $K_{2}$ is large or the spectrum is tonal). Per-band values are larger at the spectrum edges. The uncertainty field of the pressure-method results (enveloping surface and anechoic) is the expanded uncertainty $U = 2 σ_{tot}$ (95 % coverage), where $σ_{tot} = σ_{R 0}^{2} + σ_{omc}^{2}$ also folds in the operating/mounting instability $σ_{omc}$ that you estimate and pass in; the grade only bounds the method’s share of the budget.

In practice: a grade-2 $L_{W A}$ of 92.4 dB carries $U \approx 3 dB$ , so two grade-2 results 2 dB apart are statistically indistinguishable, and checking that same source against a 93 dB limit is a coin flip. Choose the grade from the decision the number has to support, not from the facility that happens to be free. And do not leave $σ_{omc}$ at its default of zero while doing so: emission.sound_power_pressure(..., omc_uncertainty=2.0) on a machine whose installation really does scatter by 2 dB turns a $U$ of 3.0 dB into 5.0 dB, and the honest number is the one the declaration has to absorb.

All these routes describe a steady source. Each formula energy-averages over an interval and reports a rate of energy flow, so it characterises the machine only if the machine is time-invariant over that interval. A cyclic machine is admissible when the averaging time spans a whole number of cycles, and the cycle then becomes part of the declared operating condition. For a single event — one press stroke, one door slam — the descriptor is not $L_{W}$ at all but the sound energy level $L_{J}$ , the same surface integral taken over the event rather than per second, defined in the same clauses of ISO 3741, ISO 3744, ISO 3745 and ISO 3746 and not implemented here. The practical test: if the A-weighted level at a fixed microphone moves by more than a few decibels over the averaging time, the source is not steady for these methods.

Two panels. Left, one measured A-weighted sound power level of 92.4 dB drawn three times with the expanded uncertainty of each accuracy grade, 1.0 dB at grade 1, 3.0 dB at grade 2 and 6.0 dB at grade 3, against a dashed declared limit of 93 dB(A) that only the grade-1 interval clears. Right, the ISO 4871 Annex B example as two stacked bars: operating mode 1 at 88 dB plus a 2 dB uncertainty giving a declared 90 dB, verified by a level of 89 dB, and operating mode 2 at 95 plus 2 giving 97 dB, not verified by a level of 98 dB

What the grade buys, and what the declaration has to absorb. The left bar is the width the method contributes; the right panel is the same width turned into $K_{W A}$ and added to the measured value, which is why a wide grade produces a high declared limit and a machine that is easy to declare.

Show the code for this figure

import matplotlib.pyplot as plt
import numpy as np

# The interval each grade puts around one measured LWA, through the library's
# own uncertainty combination; then the ISO 4871 Annex B declaration.
fig, (axl, axr) = plt.subplots(1, 2, figsize=(12, 5.2))
for k, (name, sigma_r0) in enumerate([("Grade 1", 0.5), ("Grade 2", 1.5),
                                      ("Grade 3", 3.0)]):
    u = float(emission.precision_uncertainty(sigma_r0, 0.0, 2.0))
    axl.errorbar([k], [92.4], yerr=[[u], [u]], fmt="o", capsize=10)
axl.axhline(93.0, linestyle="--")
axl.set(ylabel="LWA [dB re 1 pW]", ylim=(84.0, 101.0))

for k, (level, k_wa, l1) in enumerate([(88.0, 2.0, 89.0), (95.0, 2.0, 98.0)]):
    axr.bar([k], [level], width=0.5)
    axr.bar([k], [k_wa], width=0.5, bottom=level)
    axr.plot([k], [l1], "D", markersize=10)
axr.set(ylabel="A-weighted sound power level [dB]", ylim=(80.0, 106.0))
plt.show()

Declaring the noise emission (ISO 4871)

A measured sound power level is not yet a declaration. ISO 4871:1996 is the standard for the noise-emission declaration a manufacturer prints in technical documents: which quantities are stated, in which form, and how a declared value is verified. The preferred quantity is the A-weighted sound power level $L_{W A}$ , optionally accompanied by the A-weighted emission sound pressure level $L_{p A}$ at a work station.

A declaration takes one of two alternative forms (clause 4):

the dual-number form (clause 3.16): the measured value $L_{W A}$ and its uncertainty $K_{W A}$ stated together but separately; and
the single-number form (clause 3.15): the derived declared value $L_{W A d} = L_{W A} + K_{W A}$ , an upper limit that repeated measurements are unlikely to exceed at the stated confidence level.

$K_{W A}$ combines the measurement (reproducibility) and, for a batch, the production spread; for a single machine $K = 1.645 σ_{R}$ (Annex A.2.2), where 1.645 is the 95 % one-sided quantile of the normal distribution — the declared value is an upper limit, so only one tail is being covered. A NoiseEmissionDeclaration holds one or more per-operating-mode declarations and renders the ISO 4871 fiche through .report(). The quickest route is to declare() straight from a measured sound power:

import numpy as np
import phonometry as ph
from phonometry import ReportMetadata

# ... a measured LWA from ISO 3744 ...
result = ph.sound_power_pressure(levels, "hemisphere", radius=1.0,
                                 frequencies=freqs)

declaration = result.declare(
    uncertainty=2.0,                 # K_WA in dB (defaults to the expanded U)
    machine="Type 990, Model 11-TC",
    operating_conditions="50 Hz, 230 V, rated load",
    basic_standards="ISO 3744",
    verification_level=result.sound_power_level_a,  # L_1 for clause 6.2
)
declaration.report(
    "iso4871.pdf",
    metadata=ReportMetadata(measurement_standard="ISO 3744"),
)   # -> L_WAd = L_WA + K_WA, verified when L_1 <= L_WAd

Or build the declaration directly, reproducing the ISO 4871 Annex B example (two operating modes, $L_{W A} = 88$ and 95 dB with $K_{W A} = 2$ dB, giving declared $L_{W A d} = 90$ and 97 dB):

mode1 = ph.OperatingModeDeclaration(
    "Operating mode 1", sound_power_level=88.0, sound_power_uncertainty=2.0,
    emission_pressure_level=78.0, emission_pressure_uncertainty=2.0,
    verification_level=89.0,          # passes: 89 <= 90
)
mode2 = ph.OperatingModeDeclaration(
    "Operating mode 2", sound_power_level=95.0, sound_power_uncertainty=2.0,
    emission_pressure_level=86.0, emission_pressure_uncertainty=2.0,
    verification_level=98.0,          # fails: 98 > 97
)
ph.NoiseEmissionDeclaration(
    (mode1, mode2), machine="Type 990, Model 11-TC",
    basic_standards=("ISO 3744", "ISO 11202"), form="dual-number",
).report("iso4871.pdf")

Verifying a declared value

Verification is a separate measurement, made by somebody else. One machine of the declared type is measured, giving a single level $L_{1}$ , and the declaration holds when $L_{1}$ does not exceed the declared value (clause 6.2). That is the verification_level argument — a number the manufacturer does not supply.

What makes such a measurement admissible is clause 6.1, and it is the part most often skipped: the verification shall follow the same noise test code as the declaration or, where none exists, a basic determination standard of accuracy grade at least equal to the one behind the declared value, under identical operating and mounting conditions. A lower grade may be used only by agreement between manufacturer and user, and the difference in accuracy accounted for. Without that, the comparison is measuring the procedure and not the machine.

The rounding is a trap of its own. A single-number declaration is verified against $L_{W A d}$ , the unrounded sum $L_{W A} + K_{W A}$ rounded once; a dual-number declaration is verified against $round (L_{W A}) + round (K_{W A})$ , which can differ by a whole decibel. The library exposes both verdicts separately — verified for the single-number rule and verified_dual for the dual-number one — so a dual-number declaration must be read from the second, not from the first.

One caveat on the first snippet above: it passes verification_level=result.sound_power_level_a, which verifies the declaration against the very value it was built from. That always passes and is an illustration of the plumbing, not of a verification.

The other two arguments deserve their provenance. emission_pressure_level is the A-weighted emission sound pressure level $L_{p A}$ at the work station, determined by ISO 11201 (essentially free field), ISO 11202 (survey, with an environmental correction) or ISO 11204 (with local corrections) — none of which is implemented here, so it arrives as a measured value from elsewhere, taken under the same installation and operating conditions as the sound power. basic_standards names the determination standards behind those two numbers, and the noise test code in the fiche footnote is the type C standard for the machine family that fixed the operating and mounting conditions and the work-station positions in the first place.

The example fiche is regenerated with make reports and kept rendered in the repository; click the preview to open the PDF.

ISO 4871 noise emission declaration example report (PDF) — Noise emission declaration fiche (NoiseEmissionDeclaration.report), the ISO 4871 Annex B dual-number table with the declared L_WAd = L_WA + K_WA and the clause 6.2 verification verdict.

What this guide covers

Covered
The ISO 3740 decision guidance condensed into the method table and the decision path, the operating and mounting conditions that precede it, what the accuracy grades claim about reproducibility, and the ISO 4871 noise-emission declaration (NoiseEmissionDeclaration, OperatingModeDeclaration, declare()): the dual- and single-number forms, $L_{W A d} = L_{W A} + K_{W A}$ and the clause 6.2 verification with both rounding rules (verified, verified_dual), rendered as the declaration fiche through .report().
Not covered
The six determinations themselves live in their method guides: the enveloping surface and the anechoic array in Sound Power by Pressure Methods, the diffuse-field method in Sound Power in the Reverberation Room, both scanning methods in Sound Power by Intensity Scanning and the surface-velocity route in Sound power from surface vibration. ISO 9614-1’s own discrete-point power summation is not implemented at all; only its field indicators are, in Sound Intensity. ISO 3743-1, ISO 3743-2 and ISO 3747, the remaining members of the ISO 3740 family, are not implemented either, and neither is the sound energy level $L_{J}$ for single events. The emission sound pressure level $L_{p A}$ that stands beside $L_{W A}$ in a declaration is consumed, not determined: ISO 11201, ISO 11202 and ISO 11204 are outside the library. ISO 4871’s batch criteria of clause 6.3 are not evaluated — only the clause 6.2 single-machine verification — and its batch statistics beyond the single-machine $K = 1.645 σ_{R}$ case (Annex A.2.2) are stated, not derived.

Quick answers

What is the difference between sound power and sound pressure?

Sound pressure depends on where you stand and on the room; sound power does not. The sound power level $L_{W}$ is the total acoustic energy per second a source radiates, referenced to $P_{0} = 1 pW$ , and it is the device-independent emission descriptor that goes on a datasheet or is checked against a noise-emission limit; ISO 3744, ISO 3741, ISO 9614-2, ISO 3745 and ISO 9614-3 all determine it.

What do the accuracy grades in sound power measurement mean?

The grade is a claim about reproducibility: $σ_{R 0}$ is the standard deviation you would see if different laboratories measured the same source, each following the standard correctly. Typical A-weighted values are $σ_{R 0} \approx 0.5 dB$ for grade 1 (ISO 3741), 1.5 dB for grade 2 (ISO 3744, ISO 9614-2) and 3 dB or more for grade 3. A grade-2 $L_{W A}$ carries $U \approx 3 dB$ , so two grade-2 results 2 dB apart are statistically indistinguishable.

How do I measure sound power when background noise cannot be switched off?

Use intensity scanning: ISO 9614-2 (grade 2 or 3) or ISO 9614-3 (grade 1, precision). Because sound intensity is the net energy flux through the measurement surface, steady extraneous noise even some 10 dB above the source is tolerated, whereas the ISO 3744 pressure method needs the background at least 6 dB below the source. The per-band field indicators then decide the grade actually achieved.

References

Beranek, L. L., & Mellow, T. J. (2012). Acoustics: Sound fields and transducers. Academic Press. https://doi.org/10.1016/C2011-0-05897-0ISBN 978-0-12-391421-7. Radiation and sound fields: the free-field and diffuse-field relations between pressure and power that the whole method family rests on.
International Organization for Standardization. (1996). Acoustics — Declaration and verification of noise emission values of machinery and equipment (ISO 4871:1996). The declaration section: the dual/single-number forms, L_WAd = L_WA + K_WA (clause 3.15) and the clause 6.2 verification.
International Organization for Standardization. (2019). Acoustics — Determination of sound power levels of noise sources — Guidelines for the use of basic standards (ISO 3740:2019). The selection guide behind 'Choosing a method': grades, environments, source-size and background criteria for the whole family.

Created and maintained by José Manuel Requena Plens ORCID All projects