EN-01Environmental & Occupational Noise
Distance Attenuation
Geometric spreading from point and line sources: the inverse-square law in practice.
Inputs
Source geometry
dB
m
m
Level at r₂
62.0dB
Change ΔL
−28.0dB
Distance ratio
25×
4.64 doublings
Spreading geometry
Level vs distance
Point (selected)Line source
§ Theory of operation
Geometric divergence
In a free field, the acoustic power leaving a source spreads over an ever-larger surface. For a small (compact) source the surface is a sphere of area 4πr², so intensity falls with 1/r², the inverse-square law. For a long line source such as a busy road, a pipeline or a train, energy spreads over a cylinder whose area grows only with r.
\begin{aligned} \text{Point source:}\quad L_2 &= L_1 - 20\,\log_{10}(r_2/r_1) \qquad (-6\ \text{dB per doubling}) \\ \text{Line source:}\quad L_2 &= L_1 - 10\,\log_{10}(r_2/r_1) \qquad (-3\ \text{dB per doubling}) \end{aligned}
When does it apply?
- Far field only. Close to a source (within a few source dimensions or about λ/2π) levels fluctuate and do not follow the law.
- Finite line sources behave like lines when you are close (r < ℓ/π) and like points when far away (r > ℓ/π).
- Large planar sources (a façade, a cooling tower intake) show almost no decay in their near field.
- Indoors, the reverberant field stops the decay beyond the critical distance, see the Sound Power calculator.
Other outdoor effects
Real outdoor propagation (ISO 9613-2) also includes atmospheric absorption, ground effect, screening by barriers and meteorological refraction. These excess attenuations add to geometric spreading and become dominant over long distances, especially at high frequencies.