Exposure at Work: Doses, Decibels and the Reference Day

An exposure is a dose spread over a reference day

Every regulation in this family expresses exposure the same way: as the total dose a person received in a day, spread over a standard 8-hour day whatever the actual shift. The reference day is what makes different jobs comparable, and it has a consequence people find surprising — a 12-hour shift at a steady level is a larger exposure than 8 hours at the same level, because the extra dose is not averaged away over a longer day.

For noise the dose is sound ENERGY multiplied by time. Each task's A-weighted level is turned back into energy, multiplied by its hours, and the tasks are summed; the total is divided by the 8-hour reference and turned back into decibels. That is the daily personal noise exposure, LEP,d, and it is what the UK and EU action and limit values are written against.

Two things follow directly. Quiet time contributes almost nothing and can be left out; and the loudest task usually decides the day, because a level 10 dB higher carries ten times the energy in the same time. Shortening the loud task moves the figure far more than anything done to the quiet ones.

Three decibels or five: two rules for the same day

Under the energy rule every 3 dB doubles the dose, so each 3 dB rise halves the time it takes to reach the same exposure: 8 hours at 85 dB(A), 4 hours at 88, 1 hour at 94. That is the physics of sound energy, and it is the exchange rate the UK, the EU, Australia and NIOSH's recommended limit all use.

OSHA's rule in the United States uses 5 dB instead — each 5 dB halves the permitted time — around a permissible exposure limit of 90 dBA for 8 hours. Its dose is the sum of each period's time divided by the time permitted at that level, as a percentage, and its time-weighted average turns that dose back into the steady level that would deliver it. OSHA also counts differently for different purposes: sound from 80 dBA up is integrated for the hearing-conservation action level of 85 dBA, but only sound from 90 dBA up counts towards the permissible limit.

The two rules agree only at their reference points and diverge quickly above them. A day at a steady 90 dBA is exactly OSHA's limit and 3 dB over the British exposure limit value; two hours at 100 dBA is an OSHA dose of 100 per cent and, on the energy rule, about eight times the dose of a full day at 85. Neither calculation is wrong — they are different rules, and a figure is only meaningful beside the rule it was worked to.

Decibels add on energy, and subtract the same way

Because a decibel is a logarithm of energy, levels cannot be added directly. Two machines at 85 dB make 88, not 170: twice the energy is 3 dB more. Ten identical machines are 10 dB more than one. The corollary is that a quieter source barely registers — one 10 dB below another adds 0.4 dB to it, one 20 dB below adds less than a twentieth of a decibel.

The same arithmetic runs backwards to separate a source from its background. A measurement near a machine includes everything else audible there; subtracting the background, measured at the same spot with the machine off, on an energy basis, leaves the machine's own contribution. The correction is only worth making in a window: when the total is less than about 3 dB above the background, a small error in either reading swings the answer by several decibels, and when it is more than 10 dB above, the correction is under half a decibel and the total already describes the source.

What reaches the ear under a protector

Hearing protectors are rated in a laboratory, with trained subjects and a perfect fit, and the ratings are then used in simple subtractions. The SNR is taken from the C-weighted level; the H, M and L values are combined into a predicted reduction that depends on how far the C-weighted level sits above the A-weighted one — a large gap means low-frequency noise, which protectors stop least well, so the L value comes into play. The US NRR is taken directly from a C-weighted level, and from an A-weighted one only after 7 dB has been subtracted from it.

Real use falls short of the laboratory, and both regulators build that in. HSE takes 4 dB off any protector's rating; OSHA's technical guidance halves the NRR-based protection. Even with the allowance the answer is an estimate, and a protector removed for a few minutes in a loud area loses much of its value over the day, because the unprotected minutes dominate the energy sum.

There is a floor as well as a ceiling. HSE advises aiming for 70 to 80 dB(A) at the ear and regards less than 70 as over-protection: a worker who cannot hear warnings or speech is more likely to lift the protector off, which costs far more than the extra rating bought.

Vibration: squared on the way in, square-rooted on the way out

Hand-arm and whole-body vibration are also doses over the 8-hour reference day, but the magnitude enters SQUARED rather than as energy on a logarithmic scale. The daily exposure A(8) is the square root of the sum of each tool's magnitude squared times its time, over 8 hours. Twice the magnitude is therefore four times the dose: the 2.5 m/s² action value takes 8 hours at 2.5 m/s², 2 hours at 5 and 30 minutes at 10. Halving a tool's vibration quarters its dose; halving its trigger time only halves it.

HSE's exposure points are the same arithmetic without the square root — two times the magnitude squared times the hours — so that a supervisor can add up a day on a card: 100 points is the action value and 400 the limit value. For whole-body vibration the measurement is made at the seat on three axes, the two horizontal ones are multiplied by 1.4 before comparison, and the highest of the three decides the day. Where the ride is dominated by shocks, the vibration dose value — the fourth power rather than the square — describes the exposure better, and it scales to a full day by the fourth root of time.

Noise that leaves the site

At a neighbour the question is not a person's dose but the level at a window, and the arithmetic is geometric spreading. Sound from one machine spreads over a growing hemisphere whose area rises with the square of the distance, so each doubling of distance takes 6 dB off: a machine reading 80 dB(A) at 10 metres, about 33 feet, reads 74 at twice that distance and 68 at four times. A manufacturer's sound power level becomes a level at distance through the same spreading, less 8 dB for the hemisphere.

Two corrections finish the prediction. A machine that works half the period contributes half the energy, 3 dB less; and a solid barrier that just breaks the line of sight is worth about 5 dB, one that hides the machine completely about 10. The items are then combined on energy, which is why the loudest machine nearest the window almost always decides the result, and why moving it or screening it achieves more than anything done to the rest.

Airborne substances: the same idea without the logarithm

Dust, fume and vapour limits are also written as doses over the 8-hour reference day, but a concentration adds linearly: the 8-hour time-weighted average is each period's concentration times its hours, summed and divided by 8, with unexposed time counted as zero. Two hours of cutting at 0.3 mg/m³ is 0.075 mg/m³ as an 8-hour average, whether the rest of the day was spent on site or not; and as with noise, a longer shift raises the figure rather than being averaged away.

Substances that act on the same organ in the same way are combined by adding each one's average as a fraction of its own limit; a sum above one means the mixture is over the combined limit even when every substance is under its own. Substances with unrelated effects are never summed, because a mixture index across them describes nothing.

Welfare counts: steps, not slopes

The facilities a site needs are read from a table rather than computed from a rate, and the tables are stepped. The British workplace code steps at fixed headcounts — up to 5 people, 25, 50, 75, 100 — and then adds one toilet and one washing station for every further 25 or part of 25. OSHA's construction table sets ratios instead: one toilet up to 20 workers, one seat and one urinal per 40 above that, and one of each per 50 from 200.

Stepped tables have edges, and the edges produce results that look wrong and are simply what the table says: under OSHA's table as written, 200 workers need fewer seats than 199, because the ratio loosens at 200. A minimum is not a target, and the count is always for the most people on site at one time, all trades together — facilities sized for the average run out on exactly the days they are needed most.

What none of these pages decides

Each calculation here is fixed by the regulation or standard that defines it, which is what makes it safe to automate. What is not fixed is everything around it: whether the measurements are representative, whether a weekly average is appropriate for a particular job, what a figure above an action value requires of an employer, and whether the controls in place are working. Those are the risk assessment's questions, and the regulations assign them to the employer and a competent person rather than to arithmetic.

So every page stops at the comparison. It reports the figure, names the value it is being read against and the rule that value comes from, and says which side of it the figure falls. It never grades a workplace and never prescribes the fix — both belong to the people who can see the work.