Noise Exposure: Method

Dose, TWA, Exchange Rates, Hearing Protectors, Weighting and Room Acoustics

What the tool answers

An industrial hygienist or a plant engineer has a day's noise exposure as a list of levels and times (a survey with a sound level meter) or as a dosimeter log, and asks four questions: is the exposure within the legal limit and the action level; how much longer may the worker stay at the present level; does the hearing protector on hand bring the exposure under the limit, and by how much; and, when the spectrum, the sources or the room are known, what the noise is made of and which control pays. The tool answers each with the formulas of the governing documents written out and the substituted numbers shown, so the page can be filed as the exposure record.

Criterion level, exchange rate and threshold

Every occupational noise criterion is a pair of numbers: the criterion level L_c, the steady A-weighted level that gives a 100 % dose over an 8-hour shift, and the exchange rate q, the number of decibels by which the level may rise when the exposure time is halved. The permitted (reference) duration at a level L is

T = 8 / 2^{(L − L_c)/q} hours,

and a day made of periods C_i at levels L_i has the dose D = 100 Σ C_i/T_i percent. A dose of 100 % is the limit. The 8-hour time-weighted average is the steady level that would give the same dose in 8 hours, TWA = (q/log₁₀ 2) log₁₀(D/100) + L_c; the constant q/log₁₀ 2 is 16.61 for a 5-dB exchange rate and 9.97, printed as 10.0, for 3 dB. The threshold is the level below which the instrument integrates nothing: a 90 dBA threshold for the OSHA PEL, 80 dBA for the OSHA hearing-conservation dose and for NIOSH and ACGIH.

• OSHA, 29 CFR 1910.95. Table G-16 permits 8 h at 90 dBA, 4 h at 95, 2 h at 100, 1 h at 105, ½ h at 110 and ¼ h or less at 115 dBA (5-dB exchange rate; the table rounds 92, 97 and 102 dBA to 6, 3 and 1½ h). Appendix A, mandatory, gives Table G-16a from 80 to 130 dBA, the dose formula and TWA = 16.61 log₁₀(D/100) + 90. Paragraph (c) requires a hearing conservation program at a TWA of 85 dBA, a dose of 50 %, computed with every level from 80 dBA integrated; paragraph (b)(1) requires feasible engineering or administrative controls when Table G-16 is exceeded, hearing protectors making up the rest; paragraph (j)(2) requires protectors to attenuate the exposure of an employee with a standard threshold shift to 85 dBA.
• NIOSH, Publication 98-126 (1998). The recommended exposure limit is 85 dBA as an 8-hour TWA with a 3-dB exchange rate: T(min) = 480 / 2^{(L − 85)/3} (Table 1-1) and TWA = 10 log₁₀(D/100) + 85 (Table 1-2). The 3-dB rate is the equal-energy rule: the dose is proportional to the acoustic energy received, so L_eq over 8 hours equals the TWA. No ceiling for continuous noise is needed because the allowed time at 115 dBA is already under 28 s; a 140 dB peak limit applies to impulsive noise.
• ACGIH TLV. The same 85 dBA and 3-dB exchange rate as NIOSH; the tool integrates from 80 dBA as dosimeters set for the TLV usually do.

The same day is tabulated under all three so the difference is visible: a shift of 95 dBA for 2 hours and 90 dBA for 3 hours is 87.5 % of the OSHA PEL (TWA 89.0 dBA) but 371 % of the NIOSH REL (TWA 90.7 dBA), because the 3-dB rate halves the permitted time at 95 dBA to 48 minutes instead of 4 hours.

Reading the exposure box

Each line is a level in dBA followed by a duration: 95 2:00, 90 3 (hours), 93 45 min, 110 30 s; text after the duration is kept as a label. A line holding a level alone is one dosimeter step of the entered length (one reading per minute, for example), so a dosimeter's level log can be pasted as it is. Levels below the threshold are listed but add nothing. The L_eq line reports the energy average of every level over the measured time, threshold or not; it is the quantity a 3-dB integrating meter displays. The remaining-time line gives T(L)(1 − D/100): how much longer the last level may continue before the dose reaches 100 %. When the measured time is less than the shift, the dose over the shift is at least the dose measured; the OSHA Technical Manual's rule of extrapolating a short sample in proportion to the shift length is a screening estimate only.

Hearing protectors and the NRR

The Noise Reduction Rating on the package is computed by 40 CFR 211.207 from laboratory attenuation data: pink noise at 100 dB in each octave band from 125 Hz to 8 kHz is C-weighted and summed (107.9 dB), the A-weighted band levels less the assumed protection value (mean attenuation minus two standard deviations) are summed, and 3 dB is subtracted for spectral uncertainty. Because the NRR is defined against a C-weighted level, it is subtracted directly from a C-weighted TWA; with A-weighted data 7 dB is taken off the NRR first (29 CFR 1910.95 Appendix B). Laboratory ratings overstate field protection, so the OSHA Technical Manual halves the (NRR − 7) for compliance estimates, and NIOSH 98-126 §1.5 derates the labelled NRR by 25 % for earmuffs, 50 % for slow-recovery foam earplugs and 70 % for all other earplugs before the 7-dB correction. For earplugs worn under earmuffs the OTM takes the higher NRR and adds 5 dB. The tool reports the attenuation credited by the chosen rule, the protected level, the protected dose and its margin, the attenuation still needed to reach the limit and the 85 dBA target, and the labelled NRR that would just give it under the same rule. The C − A method uses the spectrum when no C-weighted level was entered: L_C = TWA + (L_C − L_A) of the spectrum, and the NRR applies to it without the 7 dB. Whatever the rule, the estimate holds only for a protector fitted and worn for the whole exposure; NIOSH notes that removing a 30-dB protector for 30 minutes of an 8-hour day leaves about 15 dB.

Octave bands, A and C weighting, the long method

The A weighting approximates the ear's loudness contour at moderate levels and defines the dBA of every criterion; the C weighting is nearly flat from 63 Hz to 4 kHz and is the reference for the NRR. The tool carries the IEC 61672-1 values at the octave centres (A: −39.4, −26.2, −16.1, −8.6, −3.2, 0, +1.2, +1.0, −1.1, −6.6 dB from 31.5 Hz to 16 kHz; C: −3.0, −0.8, −0.2, 0, 0, 0, −0.2, −0.8, −3.0, −8.5 dB) and sums the corrected band levels, L_A = 10 log₁₀ Σ 10^{(L_i + A_i)/10}, as OSHA Technical Manual Appendix B.5 does with whole-decibel corrections. C − A near zero means a mid-frequency spectrum for which the NRR is a fair guide; a large C − A means low-frequency noise, against which protectors deliver less than their rating. With the protector's attenuation data (mean and standard deviation per band, as printed on the package insert) the long method (NIOSH 76-120 method #1, the octave-band method of ANSI S3.19 / S12.6) computes the protected level of this particular spectrum: each A-weighted band level less (mean − k SD), summed; k = 2 protects 98 % of a fitted population, k = 1 84 %, k = 0 is the mean. The tool also recomputes the NRR of the same data by 40 CFR 211.207 so the label can be checked; the attenuation data of Figure 2 of that regulation give 19.8 dB, labelled 20. Bands below 125 Hz, where no test data exist, take the 125 Hz attenuation and are flagged.

Several sources at a receiver

Sound levels add as energies: L = 10 log₁₀ Σ 10^L_i/10, so two equal sources add 3.0 dB, ten add 10 dB, and a source 10 dB below another adds 0.4 dB; the OTM's rule-of-thumb table (add 3 dB for a difference of 0–1 dB, 2 dB for 2–4, 1 dB for 5–9, 0 beyond) approximates the same sum. A compact source in a free field spreads spherically, 20 log₁₀(r/r_ref) or 6 dB per doubling of distance; a long line of sources (a conveyor, a road) spreads cylindrically, 10 log₁₀(r/r_ref) or 3 dB per doubling. A thin barrier between source and receiver gives the insertion loss of Maekawa's curve, IL = 10 log₁₀(3 + 20 N) with the Fresnel number N = 2δ/λ, δ being the extra path length over the top: 5 dB at grazing, about 13.6 dB at N = 1, in practice no more than 20–24 dB because of flanking and diffraction. The tool reports each source's receiver level, the sum, the dominant source and its energy share, and the level that would remain if it were silenced: the dominant source must be treated first, and treating any other cannot lower the total by more than the difference between the total and the dominant level.

Reverberant rooms

Indoors the level at a receiver is the direct field of the source plus the reverberant field sustained by the walls: L_p = L_w + 10 log₁₀(Q/(4πr²) + 4/R), with L_w the sound power level re 1 pW, Q the directivity (1 in free space, 2 on a floor, 4 at a wall–floor edge, 8 in a corner), r the distance in metres and R = Sᾱ/(1 − ᾱ) the room constant from the boundary area S and its area-weighted Sabine absorption coefficient ᾱ. In feet the term inside the logarithm is 10.76 times larger, 10.3 dB. Sabine's reverberation time is T₆₀ = 0.161 V/(Sᾱ) in metres (0.049 in feet). The two fields are equal at the critical distance r_c = √(QR/16π): inside it distance and source treatment govern, beyond it only absorption helps, and doubling R lowers the reverberant level by 3 dB. Absorption coefficients by material and band are tabulated in Harris's and Beranek's handbooks; a hard room has ᾱ ≈ 0.02–0.05, a treated one 0.2–0.4.

Limits of the tool

Levels are taken as A-weighted slow-response readings; impulsive noise, the 140 dB peak limit and 115 dBA ceiling are flagged, not integrated differently. The dose assumes the dosimeter's threshold and exchange rate; a meter set otherwise must be re-read. The Maekawa and Sabine forms are the single-figure estimates of textbook practice, not a ray-tracing or a band-by-band room model, and the barrier loss is evaluated at one frequency. The NRR rules are the regulatory estimates; fit testing of the individual worker (ANSI S12.6 method B, as NIOSH recommends) replaces them where it is available.