Distance Attenuation from a Point Source

A point source radiating into the open spreads its power over an expanding sphere, so intensity falls as the inverse square of distance and the level falls as $20\log_{10}(r_2/r_1)$. Double the distance and it is $20\log_{10}2 = 6.02$ dB, every time, from any starting level. Ten times the distance is exactly 20 dB. It is the cheapest noise control available whenever there is room for it, and the first thing to check on a site plan.

The 6 dB figure belongs to a POINT source, and the most common mistake is applying it to something that is not one. A line source — a busy highway, a run of pipe, a conveyor, a row of rooftop units read from far enough away that they merge — spreads cylindrically rather than spherically, and loses only 3 dB per doubling. Over a distance ratio of sixteen, that is 12 dB rather than 24, and the difference explains why traffic noise carries so much further than intuition predicts. A source is effectively a point once you are perhaps three times its largest dimension away from it, and close in it behaves like neither, which is why manufacturers quote levels at a stated distance rather than expecting anyone to extrapolate from the casing.

Indoors this law expires quickly. Inside the reverberation radius the direct field dominates and the 6 dB rule holds; outside it the reverberant field takes over and the level flattens out. In a hard room that transition can happen within a couple of metres of the machine, which is why distance is an outdoor and a large-space tool, and absorption is the indoor one.

Outdoors, the geometric spreading is only the first term. Real propagation adds molecular absorption by the air, which grows with frequency and with dryness and only matters over hundreds of metres; ground effect, which can add or subtract several decibels depending on whether the ground is soft or paved; barriers, which are effective only when they interrupt the line of sight and are worth roughly 5 to 20 dB; and meteorology. Wind and temperature gradients bend sound rays, and a temperature inversion on a still night refracts sound back down toward the ground — which is exactly why the neighbour who never noticed the plant during the day telephones at three in the morning. The standardised outdoor calculation, ISO 9613-2, is this spreading term plus corrections for each of those effects.