Source: https://docs.jmrp.io/phonometry/perception/hearing/hearing-protectors/ # Hearing Protectors (ISO 4869-1, -2, -3 and -6) A hearing protector is not measured on a coupler. ISO 4869-1 seats it on sixteen people and records the threshold shift each of them gets, so what comes back from the laboratory is a **distribution**: one attenuation per subject per octave band, with a spread that is often a third of the mean. ISO 4869-2 is the standard that turns that distribution into a number someone can act on, and the first thing it does is refuse to use the mean. ## Where the distribution comes from (ISO 4869-1) Each of sixteen subjects finds a threshold for one-third-octave bands of pink noise at the octave frequencies from 125 Hz to 8 kHz (63 Hz optional), with open ears and with the protector in place, and the attenuation is the difference (4.6.2): $$ A_{j,f} = L_{\mathrm{occluded},j,f} - L_{\mathrm{open},j,f} $$ Annex A models the attenuation as the measured value plus three zero-mean inputs (method, equipment, environment); within one laboratory the combined standard uncertainty is the standard deviation of the mean, $u = s/\sqrt{N}$, and $U_{95} = 2u$. ```python import numpy as np from phonometry import hearing # ISO 4869-1 Table A.3: one earmuff on sixteen subjects, 125 Hz to 8 kHz. table_a3 = np.array([ [9.6, 13.5, 27.5, 32.4, 35.2, 29.1, 28.5], [14.1, 20.2, 25.8, 32.0, 28.9, 35.3, 35.7], [21.8, 27.8, 28.3, 46.6, 37.4, 40.1, 38.7], [18.5, 22.2, 36.5, 44.8, 39.1, 30.6, 33.5], [15.6, 21.9, 31.8, 42.5, 38.9, 38.3, 37.1], [18.7, 28.6, 31.3, 39.0, 35.6, 35.3, 29.4], [23.0, 26.5, 34.0, 41.3, 40.8, 38.7, 35.9], [17.3, 21.7, 25.0, 30.7, 38.6, 37.9, 40.8], [19.4, 19.6, 28.0, 36.6, 40.7, 34.9, 39.4], [11.6, 20.4, 22.6, 38.0, 39.2, 33.9, 30.3], [20.5, 21.8, 29.2, 40.7, 36.2, 35.7, 38.4], [18.3, 19.6, 26.2, 34.6, 32.7, 34.9, 26.6], [15.1, 17.5, 30.1, 39.0, 39.4, 38.2, 39.5], [21.7, 20.8, 28.3, 39.5, 38.1, 40.0, 38.4], [15.9, 17.8, 26.0, 40.6, 38.0, 40.2, 37.2], [11.8, 18.4, 29.6, 37.2, 40.8, 36.0, 29.9], ]) reat = hearing.real_ear_attenuation(table_a3) print(np.round(reat.mean_db, 1)) # [17.1 21.1 28.8 38.5 37.5 36.2 35. ] print(np.round(reat.expanded_uncertainty_db, 1)) # [2. 1.9 1.7 2.2 1.6 1.6 2.3] # Annex B, Table B.1: a second test of the same earmuff, printed as means and U95. test_2_mean = [16.8, 21.0, 28.3, 38.2, 35.5, 34.6, 38.9] test_2_u95 = [1.6, 1.2, 1.4, 1.5, 1.5, 1.7, 2.5] difference = hearing.assess_attenuation_difference( reat, test_2_mean, second_expanded_uncertainty_db=test_2_u95 ) print(np.round(difference.criterion_db, 1)) # [2.5 2.3 2.2 2.7 2.2 2.3 3.4] print(difference.significant_frequencies) # [8000.] ``` Two means differ significantly at the 5 % level when $|m_1 - m_2| > \sqrt{U_{95,1}^2 + U_{95,2}^2}$ (B.1.2), which for two equal uncertainties is $\sqrt{2}\,U_{95}$. Tables A.2 and B.2 give typical budgets (`hearing.REAT_WITHIN_LABORATORY_UNCERTAINTY`, `hearing.REAT_BETWEEN_LABORATORY_UNCERTAINTY`), and B.1.1 evaluates the minimum difference on the rounded 2,3 dB its table prints, writing that input out: "$\sqrt{2}$ × 2,3 dB = 3,3 dB". From the unrounded 2.27 dB it is 3.21 dB. The sound field of the test room (4.2.2, with Table 1 for the rotated directional microphone) is judged by `hearing.check_reat_sound_field`, whose verdict passes only when the rotation of b) was measured as well as the positions of a). ## The distribution first (Clause 5) All three methods take a mean less a multiple of its own spread, and differ in what they take it over. The octave-band method takes it over the attenuations of each band, and the result is the assumed protection value: $$ APV_{fx} = m_f - \alpha\, s_f $$ $\alpha$ is the inverse standard normal cumulative distribution at the protection performance $x$ (Table 1), so $APV_{f84}$ with $\alpha = 1$ is the attenuation 84 % of wearers reach or beat, and $APV_{f98}$ with $\alpha = 2$ is what all but one in fifty reach. The HML and SNR methods never form that value. They rate each subject first, against the eight reference noises of Table 2 or the pink noise of Table 3, and take the same reduction over those ratings (Formulae (3) to (5) and (19)). What the three share is the choice of $x$ and its $\alpha$. ```python import numpy as np from phonometry import hearing # ISO 4869-1 attenuation: 16 subjects, eight octave bands from 63 Hz to 8 kHz. attenuation = np.array([ [4, 8, 13, 18, 20, 30, 35, 30], [6, 12, 16, 21, 29, 35, 47, 35], [10, 16, 17, 23, 25, 32, 48, 37], [3, 7, 12, 18, 20, 25, 33, 30], [8, 10, 16, 16, 25, 27, 43, 32], [4, 7, 10, 15, 19, 32, 35, 31], [5, 5, 9, 16, 20, 25, 30, 28], [15, 15, 21, 26, 25, 38, 46, 38], [5, 6, 10, 13, 19, 22, 29, 28], [9, 9, 10, 19, 20, 27, 37, 31], [9, 16, 18, 24, 25, 35, 44, 39], [5, 6, 11, 12, 17, 20, 28, 28], [7, 10, 17, 22, 25, 35, 41, 44], [6, 8, 16, 18, 19, 19, 30, 33], [10, 12, 17, 25, 28, 33, 45, 40], [12, 13, 17, 27, 29, 38, 49, 41], ], dtype=float) apv = hearing.assumed_protection_value(attenuation) # x = 84 % by default print(np.round(apv.apv, 1)) # [ 4.1 6.4 10.7 14.9 18.8 23.4 31.3 28.9] ``` *Left, the protector: the assumed protection value sits a full standard deviation below the mean, and the gap is widest where the spread is, at 4 kHz. Right, the method: the HML line and the eight reference noises it was fitted on, with the three methods' answers for the same noise.* ## Three methods, in decreasing order of what they need *One protector model on sixteen subjects, reduced three ways and met with one noise. Only the octave-band method goes through the assumed protection value; HML and SNR rate each subject first and take the spread out over those ratings, and the three land within a decibel of each other.* **The octave-band method (Clause 6)** is the most faithful and the only one that sees the shape of the noise: subtract the assumed protection value band by band from the A-weighted spectrum and sum what is left (Formula (2)). **The HML method (Clause 7)** collapses the protector to three numbers, the predicted noise level reduction it gives for reference noises whose $(L_{p,\mathrm{C}} - L_{p,\mathrm{A}})$ is $-2$, $+2$ and $+10$ dB, fitted across the eight reference spectra of Table 2. Applying them needs only the C- and A-weighted levels of the real noise, through two straight segments that meet at $+2$ dB. **The SNR method (Clause 8)** collapses it to one number against a pink noise and subtracts it from the C-weighted level. Clauses 7.3 and 8.3 both allow the unweighted level in place of the C-weighted one, which reads high for noise with a lot of very low frequency content. ```python noise = [75.0, 84.0, 86.0, 88.0, 97.0, 99.0, 97.0, 96.0] # LpA = 104, LpC = 103 dB octave = hearing.octave_band_protected_level(noise, apv) hml = hearing.hml_rating(attenuation) snr = hearing.snr_rating(attenuation) print(octave.reported_level) # 81 print(hml.reported) # (24, 18, 13) print(hearing.hml_protected_level(104.0, 103.0, hml).reported_level) # 82 print(snr.reported) # 21 print(hearing.snr_protected_level(snr, l_p_c=103.0).reported_level) # 82 ``` The three answer the same question and rarely agree exactly: 81 dB, 82 dB and 82 dB for one protector in one noise. The NOTE that closes the Introduction puts differences of 3 dB or less between comparable protectors below the resolution of the exercise. The ordering is not a ranking: the octave-band method uses more information and is the one to prefer when the spectrum is available, while HML and SNR exist precisely for when it is not. The values that enter the HML and SNR applications are the **rounded** ones: Clauses 7.2 and 8.2 round the ratings to the nearest integer, which is what a protector is published with. The octave-band method starts at 63 Hz when both the noise and the protector have data there and at 125 Hz when either does not (Clause 6); the HML and SNR computations start at 125 Hz always. One caution about the reference spectra: Annex C reprints Table 2 as its Table C.1 and the reprint disagrees with the original in two cells. Table 2 is the one that reproduces the annex's own worked results, and it is the one this library carries; the discrepancy is registered in [ERRATA](https://docs.jmrp.io/phonometry/reference/errata/). ## Active noise reduction earmuffs (ISO 4869-6) An active noise reduction earmuff adds a cancellation circuit to a passive shell, and a threshold test cannot see it. ISO 4869-6 measures the two halves on the same sixteen subjects: the ISO 4869-1 attenuation with the circuit off, in octave bands, and the active insertion loss, the level at each ear with the circuit off minus the level with it on, measured with a microphone in the ear canal in one-third-octave bands. Clause 5.5 interpolates the passive side into one-third octaves (linearly in hertz, as ISO's calculation workbook does it), keeps the ear with the lower insertion loss in each band, adds the two, folds each octave back with Formula (1) and rates the sixteen results with ISO 4869-2 at 84 %. The methods are meant for steady noise exposures and do not apply to noise with impulsive components (Clause 1). ```python # ISO 4869-6 Table A.3: the lower-ear active insertion loss, 63 Hz to 8 kHz. table_a3_anr = np.array([ [18.4, 23.9, 21.6, 5.2, -4.5, -0.2, -1.3, -1.0], [19.4, 23.0, 21.7, 5.7, -6.4, -0.4, 0.8, -1.9], [19.7, 23.1, 20.8, 3.6, -4.2, -2.9, 0.2, -0.6], [19.8, 23.1, 18.7, 2.2, -4.9, -0.5, -0.2, 0.2], [20.5, 24.5, 20.2, 3.1, -4.4, -2.9, -1.4, 0.3], [18.8, 24.4, 20.8, 3.9, -4.3, -2.6, -0.4, -0.2], [21.7, 24.4, 22.2, 4.7, -5.2, -5.1, -1.5, -0.3], [20.5, 22.7, 24.3, 8.8, -8.8, -3.1, -4.8, -0.7], [22.9, 23.2, 20.7, 5.4, -6.5, -2.8, -0.5, -1.0], [21.9, 22.9, 23.1, 8.8, -8.4, -4.9, -2.6, -0.7], [23.7, 24.6, 20.8, 3.4, -6.4, -0.1, -0.3, -0.6], [22.0, 23.9, 20.3, 3.0, -4.2, -0.8, -1.0, 0.3], [23.2, 24.3, 20.9, 4.6, -5.6, -0.1, -0.5, -1.0], [21.5, 23.5, 23.3, 5.9, -5.2, -3.1, -3.6, -1.6], [24.3, 24.2, 22.5, 4.2, -6.3, -2.5, -0.9, -0.5], [23.8, 24.9, 20.7, 3.8, -4.8, -0.5, -0.3, 0.2], ]) insertion = hearing.active_insertion_loss(table_a3_anr) print(np.round(insertion.mean_db, 1)) # [21.4 23.8 21.4 4.8 -5.6 -2. -1.1 -0.6] print(np.round(insertion.expanded_uncertainty_db, 1)) # [0.9 0.4 0.7 0.9 0.7 0.8 0.7 0.3] ``` Table A.3 prints its $u$ and $U_{95}$ rows from the rounded row above each, so six of its eight $U_{95}$ cells are a tenth above the value Annex A defines; see [ERRATA](https://docs.jmrp.io/phonometry/reference/errata/). On ISO's calculation example the circuit raises $L$ from 12 dB to 19 dB and lowers $H$ from 24 dB to 21 dB, because it adds sound from 1 kHz up (`hearing.anr_total_attenuation`), and `hearing.assess_anr_linearity` finds the highest external level at which every ear still follows the 5 dB steps of 5.4.4 within ±1 dB. ## Earmuffs on a test fixture (ISO 4869-3) ISO 4869-3 measures an earmuff without subjects: the insertion loss is the level at the microphone of an acoustic test fixture (a 135 mm cylinder, end faces 145 mm apart) without the earmuff less the level with it, in one-third-octave bands from at least 63 Hz to 8 kHz (5.4.2), $IL_f = \overline{L}_{\mathrm{open},f} - \overline{L}_{\mathrm{occl},f}$. It screens production and ageing; Clause 1 says its data are not the real-ear attenuation of the earmuff nor the protection it provides, so nothing feeds it to the ISO 4869-2 methods. ```python # An earmuff fitted three times on the fixture (5.4.3), 63 Hz to 8 kHz. bands = np.asarray(hearing.EARMUFF_TEST_BANDS_HZ) loss = np.array([7.5, 9.0, 11.0, 13.5, 16.5, 20.0, 23.5, 27.0, 30.0, 32.5, 34.5, 36.0, 37.0, 37.5, 37.0, 36.0, 35.5, 36.5, 38.0, 37.0, 35.0, 33.5]) spread = np.array([[-0.6], [0.1], [0.5]]) * np.linspace(1.0, 2.2, 22) open_level = np.full(22, 88.0) il = hearing.earmuff_insertion_loss( open_level, open_level - loss + spread, isolation_cup_levels_db=open_level - 70.0 ) print(il.reported_db[[3, 9, 12, 18]]) # [13.5 32.5 37. 38. ] print(np.round(il.expanded_uncertainty_db[[3, 12, 21]], 1)) # [1.8 1.9 2.1] ``` Annex B's uncertainty is evaluated band by band from the repetitions, with Table B.1's typical values ($u$ = 1.3 dB, $U$ = 2.6 dB, `hearing.EARMUFF_INSERTION_LOSS_UNCERTAINTY`) where they are missing. `il.plot()` draws the insertion loss as Clause 6 asks, increasing downwards on the IEC 60263 scale of 50 dB per decade, on axes it creates or is given. `hearing.check_random_incidence_field` judges the site's random-incidence field with the diffuse-field check of ISO 8253-2 and this standard's Table 1 (the fixture itself may be the directional microphone where its index of Table A.1 reaches 4 dB), `hearing.check_plane_progressive_wave` the plane wave of 5.2.3, and `hearing.verify_fixture_isolation` the fixture's isolation of 5.1.4. Table 1 prints "> 5" where 5.2.2 asks for "at least 5 dB"; the library follows the text (see [ERRATA](https://docs.jmrp.io/phonometry/reference/errata/)). ## References - International Organization for Standardization (2018). *Acoustics — Hearing protectors — Part 2: Estimation of effective A-weighted sound pressure levels when hearing protectors are worn* (ISO 4869-2:2018). [iso.org catalogue](https://www.iso.org/standard/65582.html). The implemented standard: Clauses 5 to 8 and the worked examples of Annexes A to D. - International Organization for Standardization (2018). *Acoustics — Hearing protectors — Part 1: Subjective method for the measurement of sound attenuation* (ISO 4869-1:2018). [iso.org catalogue](https://www.iso.org/standard/65581.html). Where the per-subject attenuation values come from: 4.6, Annex A, Annex B and 4.2.2 with Table 1, validated against Tables A.2, A.3, B.1 and B.2. - International Organization for Standardization (2019). *Acoustics — Hearing protectors — Part 6: Determination of sound attenuation of active noise reduction earmuffs* (ISO 4869-6:2019). The active insertion loss, its uncertainty, the total attenuation of 5.5 and the linear-operation check of 5.4.4, validated against Tables A.2 and A.3 and ISO's calculation workbook. - International Organization for Standardization (2007). *Acoustics — Hearing protectors — Part 3: Measurement of insertion loss of ear-muff type protectors using an acoustic test fixture* (ISO 4869-3:2007). The insertion loss of 5.4 with Annex B, the test site of 5.2 and the fixture's isolation of 5.1.4, validated against Tables 1, A.1 and B.1. ## Standards ISO 4869-1:2018, which measures the attenuation (4.6), gives the uncertainty of its mean (Annex A, Tables A.2 and A.3), the test of whether two measurements differ (Annex B, Tables B.1 and B.2) and the sound-field conditions of the test room (4.2.2, Table 1). ISO 4869-2:2018, which defines the assumed protection value $APV_{fx}$ (Clause 5), the octave-band method (Clause 6), the $H$, $M$ and $L$ values (Clause 7) and the single number rating $SNR$ (Clause 8). ISO 4869-6:2019, which adds the active insertion loss of an active noise reduction earmuff to that attenuation (5.4, 5.5, Annex A). ISO 4869-3:2007, which screens an earmuff by its insertion loss on an acoustic test fixture (5.4, Annex B) and qualifies the fixture and its test site (5.1.4, 5.2). ## See also - [Occupational Noise Exposure (ISO 9612)](https://docs.jmrp.io/phonometry/perception/hearing/occupational-exposure/): the daily exposure level the protected level feeds into. - [Noise-induced hearing loss (ISO 1999)](https://docs.jmrp.io/phonometry/perception/hearing/noise-induced-hearing-loss/): what the exposure the protector did not stop does over a working life. - [Hearing threshold (age and reference zero)](https://docs.jmrp.io/phonometry/perception/hearing/hearing-threshold/): the baseline any protected exposure is judged against. - [Audiometric Test Methods (ISO 8253-1 and -2)](https://docs.jmrp.io/phonometry/perception/hearing/audiometry/): the diffuse-field test the site of ISO 4869-3 shares. - API reference: [`hearing.real_ear_attenuation`](https://docs.jmrp.io/phonometry/reference/api/hearing/real-ear-attenuation/), [`hearing.hearing_protectors`](https://docs.jmrp.io/phonometry/reference/api/hearing/hearing-protectors/), [`hearing.active_noise_reduction`](https://docs.jmrp.io/phonometry/reference/api/hearing/active-noise-reduction/) and [`hearing.earmuff_insertion_loss`](https://docs.jmrp.io/phonometry/reference/api/hearing/earmuff-insertion-loss/).