Source: https://jmrplens.github.io/phonometry/devices/emission/intensity/ # Sound Intensity (p-p method) Sound *pressure* tells you how loud a point is; sound **intensity** tells you where the energy is *going*. It is the acoustic power flux (W/m²), a signed vector quantity, which is why intensity probes can localize sources, separate them from background noise and measure sound power in situ (ISO 9614) where a pressure measurement alone cannot. ## The two-microphone principle (IEC 61043) A p-p probe holds two matched microphones a small distance $\Delta r$ apart. The pressure at the probe center is their mean, and the particle velocity comes from the pressure *gradient* (Euler's equation, finite-difference form): $$ p = \frac{p_1 + p_2}{2}, \qquad u = -\frac{1}{\rho_0\ \Delta r}\int (p_2 - p_1)\ dt, \qquad I = \overline{p\ u} $$ In practice the estimator works in the frequency domain through the cross-spectrum of the two channels (the standard's equivalent form): $$ I(f) = -\ \frac{\mathrm{Im}\lbrace G_{12}(f)\rbrace}{2\pi f\ \rho_0\ \Delta r} $$ The probe itself is small enough to draw at true scale. `plot_pp_probe_geometry` puts the classic 12 mm solid spacer between the two face-to-face capsules, and a computed `IntensityResult` that retained its `spacing` redraws its own probe with `res.plot_geometry()`. *The finite difference at true scale: two half-inch capsules face to face across 12 mm of solid spacer, and that $\Delta r$ is both the sensitivity of the gradient estimate and the origin of the high-frequency error.*

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```python import matplotlib.pyplot as plt from phonometry import emission # The classic 12 mm solid spacer between two half-inch microphones. emission.plot_pp_probe_geometry() plt.show() # A computed IntensityResult retains its spacing: # res = emission.sound_intensity(p1, p2, fs, spacing=0.012) # res.plot_geometry() ```

```python import numpy as np from phonometry import emission fs = 48000 rng = np.random.default_rng(0) # The two probe-microphone pressures in Pa, p1 closest to the source. # In a real measurement these are your two calibrated probe recordings; # synthesized here (p2 = p1 delayed one sample) so the guide runs. p1 = 0.02 * rng.standard_normal(fs) p2 = np.concatenate(([0.0], p1[:-1])) # p2 = p1 delayed one sample res = emission.sound_intensity(p1, p2, fs, spacing=0.012, fraction=3, limits=[100, 2500]) print(res.total_intensity_level, res.total_direction) # LI [dB], ±1 print(res.frequency, res.intensity_level) # per band res.plot() # Lp vs LI per band + the pressure-intensity index (needs matplotlib) ``` *Left: in a plane progressive wave all pressure is transported, so $L_I \approx L_p$. Right: a standing wave carries (almost) no net energy, so the pressure is high but the intensity collapses. The gap $L_p - L_I$ is the **pressure-intensity index**, the fundamental quality indicator of every intensity measurement.*

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```python import matplotlib.pyplot as plt import numpy as np from phonometry import emission fs = 48000 rng = np.random.default_rng(0) # The two probe-microphone pressures in Pa, p1 closest to the source. # In a real measurement these are your two calibrated probe recordings; # synthesized here (p2 = p1 delayed one sample) so the guide runs. p1 = 0.02 * rng.standard_normal(fs) p2 = np.concatenate(([0.0], p1[:-1])) # p2 = p1 delayed one sample res = emission.sound_intensity(p1, p2, fs, spacing=0.012, fraction=3, limits=[100, 2500]) # res is the IntensityResult computed in the example above. # One line — Lp vs LI per band with the pressure-intensity index on a twin axis: res.plot() plt.show() # By hand, from the per-band fields the result carries — mirroring what # IntensityResult.plot() draws (bar label, merged twin-axis legend, δpI title): fig, ax = plt.subplots() ax.semilogx(res.frequency, res.pressure_level, "o-", label="Pressure level Lp") ax.semilogx(res.frequency, res.intensity_level, "s--", label="Intensity level LI") ax.set_xlabel("Frequency [Hz]") ax.set_ylabel("Level [dB]") twin = ax.twinx() twin.bar(res.frequency, res.pressure_intensity_index, width=res.frequency * 0.2, color="#2ca02c", alpha=0.25, label="δpI = Lp − LI") twin.set_ylabel("Pressure-intensity index δpI [dB]") # Merge both axes' handles into a single legend, exactly as .plot() does: lines, labels = ax.get_legend_handles_labels() tlines, tlabels = twin.get_legend_handles_labels() ax.legend(lines + tlines, labels + tlabels) ax.set_title(f"Lp vs LI (total δpI = {res.total_pressure_intensity_index:.1f} dB)") plt.show() ```

The same contrast plays out dynamically below: the pressure and velocity phasors of a progressive and a standing wave, with the instantaneous intensity averaging to a net flow in one case and to zero in the other. [Watch the high-resolution video (WebM)](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/anim_instantaneous_intensity.webm) ## Knowing when to trust the number Two physical limits bound every p-p measurement, and the result object carries both: - **High frequency**: the finite-difference gradient underestimates $I$ by $\sin(k\Delta r)/(k\Delta r)$, verified in CI against IEC 61043 Table 3. `IntensityResult.bias_correction` provides the factor and `max_valid_frequency` ($\approx 0.1\,c/\Delta r$; 2.9 kHz for a 12 mm spacer) the practical ceiling. Larger spacers reach lower frequencies, smaller ones higher. - **Reactive fields**: when `pressure_intensity_index` ($F_2$ in ISO 9614-1) approaches the probe's residual index $\delta_{pI0}$, phase errors dominate. Before any of that, ISO 9614-1 asks a question about the *field* rather than the surface: is it steady enough to be scanned at all? In the initial test (clause 8.2) one typical position is picked on an initial measurement surface and the normal intensity is sampled there $M$ times with a short averaging time (Note 9 suggests $M = 10$, and, for periodic signals, 8 s to 12 s per sample or any whole number of cycles). **$F_1$**, the temporal variability indicator, is the coefficient of variation of those samples (equations (A.1)–(A.2)), so it is zero for a perfectly steady field and grows as the extraneous intensity wanders. Table B.3 asks for action code (e) above $F_1 > 0.6$: reduce the variability, measure during quieter periods, or lengthen the averaging time at each position. Annex B also has it evaluated immediately before and after the measurement on any one surface (B.1.4). ```python from phonometry import emission # The M short-time samples of the normal intensity at one fixed position (W/m²). samples = [1.20e-5, 0.94e-5, 1.51e-5, 1.08e-5, 1.33e-5, 1.02e-5, 1.44e-5, 1.17e-5, 0.88e-5, 1.29e-5] f1 = emission.temporal_variability_indicator(samples) print(round(f1, 3)) # 0.177, a steady field # Or carried on the surface result alongside F2/F3/F4, by handing the same # samples to field_indicators together with the per-position scan below: fi = emission.field_indicators([74.1, 73.8, 74.5, 73.2], [1.2e-5, 1.0e-5, 1.4e-5, 0.9e-5], temporal_intensity=samples) print(fi.field_is_stationary()) # True (Table B.3 limit 0.6) ``` Over a measurement surface, the remaining ISO 9614-1 Annex A field indicators grade the scan itself. **$F_2$**, the surface pressure-intensity indicator, is the surface pressure level minus the level of the mean *magnitude* of the normal intensity: the larger it is, the closer the measurement sits to the probe's phase-error floor. **$F_3$**, the negative partial power indicator, is the same difference taken with the *signed* mean intensity: $F_3 - F_2 > 0$ reveals power flowing inward through parts of the surface. **$F_4$**, the field non-uniformity indicator, is the normalised spread of the per-position intensities: the larger it is, the more measurement positions the surface needs. Together with the dynamic-capability criterion they are available directly: ```python import numpy as np from phonometry import emission # Per-position measurements over the ISO 9614-1 measurement surface pressure_levels = np.array([74.1, 73.8, 74.5, 73.2]) # Lp per position (dB) normal_intensity = np.array([1.2e-5, 1.0e-5, 1.4e-5, 0.9e-5]) # signed In per position (W/m²) fi = emission.field_indicators(pressure_levels, normal_intensity) print(round(fi.f2, 2), round(fi.f3, 2), round(fi.f4, 3)) # 3.41 3.41 0.197 ld = emission.dynamic_capability_index(18.0) # δpI0 = 18 dB → Ld = δpI0 − K print(ld, ld > fi.f2) # 8.0 True (criterion 1) ``` With 2D `(positions, bands)` arrays and the band centres the indicators come back **per band**, and the result is plottable in one line, the form in which the criteria are actually checked (each band passes or fails on its own): ```python fi = emission.field_indicators(lp_bands, in_bands, freqs) # (positions, bands) fi.plot(dynamic_capability=ld) # F2/F3 per band vs Ld, F4 on a twin axis (needs matplotlib) ``` *$F_2$ climbs towards low frequency as the field turns reactive, and at 125 Hz it crosses the instrument's dynamic capability $L_\mathrm{d} = \delta_{pI0} - K$: that band fails criterion 1, and no averaging will fix it — it calls for a larger spacer, a different surface or a quieter room. $F_3$ rising above $F_2$ in the same band reveals inward-flowing (negative) partial intensity, and the $F_4$ bars set the number of positions the surface needs (criterion 2, $N > C \cdot F_4^2$).*

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```python import matplotlib.pyplot as plt import numpy as np from phonometry import emission # A 10-position discrete-point scan over six octave bands: the surface # pressure is nearly uniform, and the normal intensity per band is set so the # field turns reactive towards low frequency, with two inward-flowing # positions in the 125 Hz band (rescaled so the band mean keeps its target). freqs = np.array([125.0, 250.0, 500.0, 1000.0, 2000.0, 4000.0]) delta_pi = np.array([10.5, 8.5, 6.0, 4.5, 3.5, 3.0]) # target Lp − L|In| rng = np.random.default_rng(9614) lp_bands = 78.0 + rng.normal(0.0, 0.4, (10, freqs.size)) i_mean = 10.0 ** ((78.0 - delta_pi) / 10.0) * 1.0e-12 in_bands = i_mean[None, :] * (1.0 + rng.normal(0.0, 0.18, (10, freqs.size))) in_bands[:2, 0] = -0.35 * i_mean[0] in_bands[2:, 0] *= (10.0 * i_mean[0] - in_bands[:2, 0].sum()) / in_bands[2:, 0].sum() fi = emission.field_indicators(lp_bands, in_bands, freqs) ld = emission.dynamic_capability_index(18.0) # δpI0 = 18 dB, K = 10 dB # One line — F2/F3 per band against Ld, with F4 on a twin axis: fi.plot(dynamic_capability=ld) plt.show() # By hand, from the per-band fields the result carries — mirroring what # FieldIndicators.plot() draws (Ld step line, merged twin-axis legend): fig, ax = plt.subplots() ax.plot(fi.frequency, fi.f2, "o-", label="F2 (surface pressure-intensity)") ax.plot(fi.frequency, fi.f3, "s--", label="F3 (negative partial power)") ax.plot(fi.frequency, np.full(fi.frequency.size, ld), ":", drawstyle="steps-mid", label="Dynamic capability Ld") ax.set_xlabel("Frequency [Hz]") ax.set_ylabel("Indicator [dB]") twin = ax.twinx() twin.bar(fi.frequency, fi.f4, width=fi.frequency * 0.2, alpha=0.25, color="#2ca02c", label="F4 (non-uniformity)") twin.set_ylabel("Field non-uniformity F4") lines, labels = ax.get_legend_handles_labels() tlines, tlabels = twin.get_legend_handles_labels() ax.legend(lines + tlines, labels + tlabels) plt.show() ```

[Watch the high-resolution video (WebM)](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/anim_intensity_scan_power.webm) ### The margin over the residual index The two channels of any real probe and analyzer are never perfectly phase matched. Feed both channels the *same* signal (the residual-intensity test of IEC 61043): the true intensity is exactly zero, yet the mismatch reports a small false intensity. The gap between the pressure level and that false intensity level is the **residual pressure-intensity index** $\delta_{pI0}$, the instrument's phase-error floor expressed as an index; IEC 61043 grades probes and processors (class 1 / class 2) chiefly by it. In the field, the measured index $\delta_{pI} = L_p - L_I$ says how far the pressure level stands above the level of the net flow, and the systematic error of the intensity estimate is bounded by the margin between the two indices: $$ \varepsilon = 10 \log_{10}\!\left( 1 \pm 10^{(\delta_{pI} - \delta_{pI0})/10} \right) $$ A 10 dB margin keeps the bias within about 0.5 dB and a 7 dB margin within about 1 dB; these are precisely the bias factors $K$ of ISO 9614, and the **dynamic capability** $L_\mathrm{d} = \delta_{pI0} - K$ is the largest field index the instrument can afford at a given grade. Read it as a budget: every decibel the field's $\delta_{pI}$ rises spends a decibel of margin, and when $\delta_{pI}$ reaches $\delta_{pI0}$ the reading is pure phase error, of either sign. This is why the pressure-intensity index, not the microphone quality, gates the achievable accuracy of every intensity measurement. ### Grading the instrument: IEC 61043 Table 2 $\delta_{pI0}$ is not just a number to subtract $K$ from; it is what IEC 61043 grades the hardware by. Table 2 of the standard sets a **minimum** $\delta_{pI0}$ in every one-third-octave band from 50 Hz to 6.3 kHz, separately for a **probe**, a **processor** and a **complete instrument**, in class 1 and class 2, printed for the nominal 25 mm microphone separation. Note 1 rescales the whole table for any other spacer by $+10\log_{10}(x/25)$ with $x$ in millimetres, which is the same 3 dB per doubling the previous section arrived at from the physics. `intensity_class_compliance` compares a measured $\delta_{pI0}$ spectrum against both masks band by band and returns the class the chain actually meets: the loosest class every band clears, or `None` when some band clears neither: ```python from phonometry import metrology # The band centres Table 2 is defined on, and the measured residual index of # the chain: one value per band, taken with the spacer that will be fitted in # the field. Replace the placeholder with your own residual-intensity test. freqs, _, _ = metrology.residual_index_limits("instrument", spacing=0.012) measured_delta_pi0 = [11.0, 11.9, 11.2, 10.0, 13.2, 15.9, 17.0, 18.0, 19.0, 20.0, 21.0, 22.0, 23.0, 24.0, 24.0, 24.0, 24.0, 24.0, 24.0, 24.0, 24.0, 24.0] # dB, 22 bands res = metrology.intensity_class_compliance(measured_delta_pi0, freqs, device="instrument", spacing=0.012) print(res.overall_class) # 2: one band misses the class 1 minimum print(res.binding_margin()) # smallest per-band margin to that class [dB] print(res.failing_bands(1)) # the band centres that cost it class 1 [Hz] res.plot() # measured δpI0 over the two Table 2 masks res.report("verification.pdf") # one-page verification fiche (PDF) ``` *Both Table 2 masks come down by $10\log_{10}(12/25) = -3.2\ \text{dB}$ for the 12 mm spacer. The measured index climbs 10 dB per decade at low frequency, parallel to the requirement, because a channel phase mismatch that is constant in degrees buys exactly that slope; it flattens above 1 kHz where the mismatch of a real chain starts growing with frequency instead. A vent resonance around 100 Hz costs 4 dB and drops that one band below the class 1 minimum, so the whole chain is graded class 2.*

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```python import matplotlib.pyplot as plt import numpy as np from phonometry import metrology # A complete instrument with the common 12 mm spacer. The measured index is # modelled from the physics behind Table 2: a residual phase mismatch φs reads # as δpI0 = 10 lg(kd/φs), so a mismatch that is constant in degrees already # climbs 10 dB per decade, and above 1 kHz the mismatch of a real chain grows # with frequency, so the index levels off. spacing = 0.012 freqs, _, _ = metrology.residual_index_limits("instrument", spacing=spacing) phase_mismatch = 0.05 * np.maximum(1.0, freqs / 1000.0) # degrees measured = metrology.residual_index_from_phase_mismatch(phase_mismatch, freqs, spacing) measured = measured - 4.0 * np.exp(-((np.log(freqs / 100.0) / 0.25) ** 2)) res = metrology.intensity_class_compliance(measured, freqs, spacing=spacing) res.plot() plt.show() ```

Two companion rules of the standard come with it. Clause 6.1 fixes the frequency range a class attests: 45 Hz to 7.1 kHz in one-third octaves, which class 1 requires and class 2 may also use, or 45 Hz to 5.6 kHz in octaves, which is offered to class 2 as an alternative. A verdict computed over fewer bands is flagged `range_limited` so it cannot be read as a full-range claim. The Spanish translation UNE-EN 61043:1999 records only the octave alternative for class 2 and drops the one-third-octave one; the library follows the EN/IEC text (see the [errata registry](https://jmrplens.github.io/phonometry/reference/errata/)). Clause 8 combines separately supplied components: `instrument_class_from_components(probe_class, processor_class)` returns 1 only when both are class 1, and 2 for every other pairing. The example fiche, regenerated with `make reports`, is kept rendered in the repository. Click the preview to open the PDF: [](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/reports/iec61043_intensity_example.pdf) ### Reading `δpI0` as a phase error The requirement is really a phase-matching requirement in disguise. In an axially propagating plane wave the *true* phase difference across the spacer is $kd$, so a residual intensity produced by a channel mismatch $\varphi_s$ gives $$ \delta_{pI0} = 10 \log_{10}\!\left( \frac{k d}{\varphi_s} \right) $$ and the two conversions run both ways: ```python from phonometry import metrology # 20 dB of residual index at 1 kHz over a 25 mm spacer: phi = metrology.phase_mismatch_from_residual_index(20.0, 1000.0, 0.025) print(round(float(phi), 2)) # 0.26 degrees, a hundredth of kd # And back, for a chain whose channels are matched to 0.05°: print(round(float(metrology.residual_index_from_phase_mismatch( 0.05, 1000.0, 0.012)), 1)) # 24.0 dB ``` That is why the low-frequency end of Table 2 rises 1 dB per third-octave band and then flattens: below the knee the standard is asking for a *constant* phase match, and above it for a constant index. The knee sits at 250 Hz for the three class 1 columns and for the class 2 processor, and at 630 Hz for the class 2 probe and the class 2 complete instrument, which is also where the table stops stepping in whole decibels (the instrument goes 14 dB at 315 Hz, 14,5 dB at 400 Hz, 15 dB at 500 Hz). It is also why a tenth of a degree of channel mismatch is a demanding specification, and why a probe must be verified with the spacer it will actually be used with. ### Reactive fields near sources Close to a source the field turns **reactive**: pressure and particle velocity drift toward quadrature, so a large pressure carries little net flow. For a small source the quadrature component grows as $1/(kr)$; at 100 Hz and 0.25 m from the source it is already about twice the active one, and $\delta_{pI}$ climbs just as it does in the standing wave of the figure above. The same happens between a machine and a hard reflecting surface, and in reverberant rooms where the diffuse field raises pressure without transporting energy outward. This is why ISO 9614-1 keeps the measurement surface on average more than 0.5 m away from the source, and why, when a scan fails the dynamic-capability criterion, moving the surface outward or adding absorption to the room usually lowers $F_2$ below $L_\mathrm{d}$ more cheaply than better hardware. ### Choosing the spacer The spacer sets both ends of the usable band, in opposite directions: - **The top end is geometry.** The finite difference underestimates the gradient by $\sin(k\Delta r)/(k\Delta r)$, so the ceiling scales as $1/\Delta r$: `max_valid_frequency` $\approx 0.1\,c/\Delta r$ keeps the bias within about 0.3 dB, giving roughly 5.7 kHz for a 6 mm spacer, 2.9 kHz for 12 mm and 690 Hz for 50 mm (`bias_correct=True` undoes the known bias somewhat beyond that). - **The bottom end is phase.** A progressive wave puts only $360\,f\,\Delta r/c$ degrees of true phase across the spacer, 0.8° at 63 Hz over 12 mm, while the channel mismatch stays fixed. Lowering the frequency shrinks the signal, not the error, so the margin over $\delta_{pI0}$ collapses at low frequency. A larger spacer buys back that margin: the IEC 61043 residual-index requirements scale as $10\log_{10}(\Delta r/25\ \text{mm})$, so doubling the spacer is worth 3 dB of low-frequency margin. No single spacer covers the full audio range: 6 mm suits high-frequency work, 50 mm low-frequency work, and the common 12 mm covers the mid band. Wide-band surveys are measured twice with two spacers and the band results merged; whichever spacer is fitted, verify $\delta_{pI0}$ with that spacer in place, since the index belongs to the probe-spacer-analyzer chain, not to the microphones alone. ### `sound_intensity()` parameters | Parameter | Type | Units | Range / default | Notes | | :--- | :--- | :--- | :--- | :--- | | `p1`, `p2` | 1D arrays | Pa | equal length | Microphone closer to the source first; reversing them flips the sign | | `fs` | int | Hz | > 0 | | | `spacing` | float | m | > 0 | Microphone separation $\Delta r$ (typ. 6/12/50 mm) | | `rho` | float | kg/m³ | default `1.204` | Air density | | `c` | float | m/s | default `343.0` | Speed of sound (bias/validity estimates) | | `fraction` | int, optional | — | `1`, `3` or `None` (default) | Octave/third-octave band integration | | `limits` | list, optional | Hz | default library band range | Band analysis limits | | `bias_correct` | bool | — | default `False` | Apply the per-bin $(k\Delta r)/\sin(k\Delta r)$ correction (IEC 61043 §7.3) before summing, so band/broadband totals stop under-reading as $f \to$ `max_valid_frequency`; bins past the first null are left uncorrected. The per-band `bias_correction` factor is reported either way | See [Theory](https://jmrplens.github.io/phonometry/reference/theory/signal-analysis/) for the derivations and [Calibration](https://jmrplens.github.io/phonometry/signals/metrology/calibration/) for absolute scaling of the two channels. ## See also - [Sound Power by Intensity Scanning](https://jmrplens.github.io/phonometry/devices/emission/sound-power-intensity/) — the ISO 9614-2/-3 routes that consume $\delta_{pI}$, the field indicators and the dynamic capability. - [Sound Power](https://jmrplens.github.io/phonometry/devices/emission/sound-power/) — choosing between the intensity, pressure and reverberation-room routes. - [Sound power from surface vibration](https://jmrplens.github.io/phonometry/devices/emission/vibration-sound-power/) — the ISO/TS 7849-2 radiation factor needs an intensity-measured power. - [Calibration](https://jmrplens.github.io/phonometry/signals/metrology/calibration/) — the absolute scaling of the two channels the estimator assumes. - [Theory: signal analysis](https://jmrplens.github.io/phonometry/reference/theory/signal-analysis/) — the cross-spectral derivation behind $I(f) = -\mathrm{Im}\{G_{12}\}/(2\pi f \rho_0 \Delta r)$. - API reference: [`emission.intensity`](https://jmrplens.github.io/phonometry/reference/api/power/intensity/). - Theory: [Sound intensity (IEC 61043)](https://jmrplens.github.io/phonometry/reference/theory/signal-analysis/#sound-intensity-iec-61043): the finite-difference approximation behind a p-p probe and the errors it commits. ## References - Fahy, F. J. (1995). *Sound intensity* (2nd ed.). E&FN Spon. ISBN 978-0-419-19810-9. [doi:10.4324/9780203475386](https://doi.org/10.4324/9780203475386). The monograph on the subject: active and reactive intensity, the p-p estimator and the phase-mismatch error budget behind this page. - International Electrotechnical Commission. (1993). *Electroacoustics — Instruments for the measurement of sound intensity — Measurements with pairs of pressure sensing microphones* (IEC 61043:1993; adopted in Europe as EN 61043:1994). [IEC webstore](https://webstore.iec.ch/en/publication/4353). The instrument standard: the cross-spectral estimator, the residual-intensity test behind $\delta_{pI0}$, the Table 2 minima per band for probes, processors and instruments with the $+10\log_{10}(x/25)$ separation rule (Note 1), the frequency ranges of clause 6.1 and the component-combination rule of clause 8. - International Organization for Standardization. (1993). *Acoustics — Determination of sound power levels of noise sources using sound intensity — Part 1: Measurement at discrete points* (ISO 9614-1:1993). [iso.org catalogue](https://www.iso.org/standard/17427.html). The field indicators $F_1$ to $F_4$, the dynamic-capability criterion and the 0.5 m surface-distance rule. ## Standards IEC 61043:1993 (EN 61043:1994), *Electroacoustics — Instruments for the measurement of sound intensity — Measurements with pairs of pressure sensing microphones*: the two-microphone cross-spectral intensity estimator, the finite-difference bias correction and the usable-bandwidth bound (clause 7.3, Table 3), the minimum pressure-residual intensity index per band for probes, processors and instruments in class 1 and class 2 with its separation rule (Table 2 and its Note 1), the processor frequency ranges (clause 6.1) and the class of an instrument assembled from separate components (clause 8). ISO 9614-1:1993, *Acoustics — Determination of sound power levels of noise sources using sound intensity — Part 1: Measurement at discrete points*: the pressure-intensity index, the Annex A field indicators $F_1$ (equations (A.1)–(A.2), evaluated in the initial test of clause 8.2 and again per Annex B, B.1.4), $F_2$, $F_3$ and $F_4$, the Table B.3 temporal-variability limit and the dynamic-capability criterion (Annex B). **Not covered.** ISO 9614-1's own sound-power determination, clauses 8 and 9, which sums the partial powers $I_i S_i$ over the discrete points into $L_W$, is not implemented: `sound_intensity` and `field_indicators` report intensity and field quality, not a summed power. The scanning routes that do compute $L_W$ from intensity, ISO 9614-2 and **ISO 9614-3**, are in [Sound power by intensity scanning](https://jmrplens.github.io/phonometry/devices/emission/sound-power-intensity/). The residual- intensity *test* of IEC 61043 is not performed here either: $\delta_{pI0}$ is a value the caller measures on their own probe-and-analyser chain, with the spacer that will be fitted, and supplies — what the library does with the number is grade it against Table 2. The before-use check of clause 14 and the ISO 9614-2 probe-reversal test are procedures, not functions.