Why they do not add
A decibel is ten times the log of an energy ratio, so levels do not add — the energies behind them do. Convert each level to an energy, sum, convert back. Two identical sources double the energy, and ten times the log of two is 3.01, so the pair reads three decibels above one of them. Four is 6.02. Ten is exactly 10. A hundred is exactly 20.
Run the other way it explains a lot of frustrated site visits. Turning off one of four identical condensers takes the total from four units to three, which is ten times the log of three quarters, or 1.2 dB. Nobody hears that. Turning off two of the four is 3 dB, which is just about detectable. The arithmetic is why partial shutdowns never settle a complaint.
The loudest source is almost the whole answer
Work the defaults: a condenser at 72, a pool pump at 65 and two heat pumps at 68, all measured at three feet, carried out to fifty feet at six decibels per doubling. The condenser lands at 47.7, the pump at 40.7, the pair of heat pumps at 46.7, and the three together come to 50.6. Add a 45 dB background and the meter reads 51.7.
Now take the condenser out entirely. The total falls to 47.6 — three decibels. Quieten it by ten decibels instead of removing it and the total falls to 48.0, which is 2.6 of the ten you paid for. Everything else in the list is holding the floor up. That is the pattern to look for before writing a specification: rank by the share of energy column, and if the top row carries less than about two thirds of the total, fixing it alone will disappoint.
Distance, honestly
A point source radiating freely loses six decibels every time the distance doubles, because the same energy is spread over a sphere four times the area. A line of sources — a road, a rail line, a long row of units — loses three, because the geometry is cylindrical rather than spherical. Real sites sit between the two and rarely match either.
What pushes the real figure away from the law is everything the law ignores. Hard ground reflects and the level falls more slowly. Soft ground, long grass and dense planting take more out, though far less than people hope: a hedge is a visual barrier and barely an acoustic one. A solid wall or a building either blocks the line of sight, in which case the attenuation depends on how far the sound has to bend around the top, or it reflects, in which case a source can be louder behind a reflective surface than in the open. None of that is in this page, and all of it is measurable on the actual site.
Levels, limits and what this page will not do
The last block subtracts one number from another and says so. It is not a compliance check and it is not capable of being one. An ordinance specifies which weighting applies, over what averaging period, measured where, under what weather, with what penalty for tonal or impulsive character, and by whom — and two jurisdictions twenty miles apart routinely differ on every one of those. A number that clears the limit in the arithmetic here can fail the actual measurement, and the reverse happens too.
The same caution applies to the levels going in. A submittal quoting a sound power level is describing the total energy a machine radiates and is not a level at a distance; the two get confused constantly and the difference runs to double figures. Check which one you have before typing it into the form.
Questions people ask
Do two 70 dB machines make 73 or 140?
Seventy three. Decibels are a logarithm, so what adds is the energy behind them rather than the numbers. Doubling energy is ten times the log of two, which is 3.01 dB. Ten identical machines add exactly 10 dB, and a hundred add exactly 20 — the table on the page prints the whole progression.
How much does switching one unit off help?
Less than anyone expects unless it was the loudest. One out of four identical units is 1.2 dB, which is below what most people notice. Two out of four is 3 dB. With mixed sources it depends entirely on the share of energy each one carries, which is the last column of the table — if the top row is not carrying most of the total, removing it will disappoint.
Six decibels per doubling or three?
Six for a single machine radiating freely, because the energy spreads over a sphere. Three for a long line of sources such as a road, because the geometry is cylindrical. Actual sites fall between and are affected by ground reflection, which slows the falloff, and by soft ground and planting, which speeds it slightly. If the answer matters, measure at the position it matters at.
Can I put a sound power level in the level column?
No, and the mistake is common enough to be worth checking twice. A sound power level describes the total energy a machine radiates and has no distance attached; a sound pressure level is what a meter reads at a stated distance, and that is what this column wants. The gap between them runs into double figures, so mixing them produces an answer that is wrong by more than any of the modelling assumptions.
Does this tell me if I am within the noise limit?
No. It subtracts your figure from the total and stops there. Which weighting, which averaging period, measured where and by whom, with what allowance for tonal character — all of that is set by the ordinance and by whoever enforces it, and none of it is in this arithmetic. Read the ordinance and ask the enforcing body.