Source: https://jmrplens.github.io/phonometry/perception/hearing/hearing-protectors/ # Hearing Protectors (ISO 4869-2) A hearing protector is not measured on a coupler. ISO 4869-1 seats it on at least 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. ## The distribution first (Clause 5) Every method starts from the assumed protection value, the mean attenuation reduced by a multiple of its own spread: $$ APV_{fx} = m_f - \alpha\, s_f $$ $\alpha$ 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. ```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 **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 $(L_{p,C} - L_{p,A})$ 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. ```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. Clause 1's own NOTE 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://jmrplens.github.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. ## Standards 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). The attenuation they all start from is measured to ISO 4869-1:2018. ## See also - [Occupational Noise Exposure (ISO 9612)](https://jmrplens.github.io/phonometry/perception/hearing/occupational-exposure/): the daily exposure level the protected level feeds into. - [Noise-induced hearing loss (ISO 1999)](https://jmrplens.github.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://jmrplens.github.io/phonometry/perception/hearing/hearing-threshold/): the baseline any protected exposure is judged against. - API reference: [`hearing.hearing_protectors`](https://jmrplens.github.io/phonometry/reference/api/hearing/hearing-protectors/).