Noise Distance Attenuation

Why doubling the distance reduces sound by 6 dB (point source)

A point source radiates sound energy uniformly in all directions, creating a spherical wavefront. The acoustic intensity — power per unit area — is distributed over the surface of that sphere. Since the surface area of a sphere grows as the square of the radius (A = 4πr²), doubling the distance quadruples the area over which the same total power is spread. Because intensity is inversely proportional to distance squared, this is the inverse-square law.

In decibels, intensity is: L = 10 × log₁₀(I/I₀). When distance doubles, intensity is divided by 4, so the change in level is: ΔL = 10 × log₁₀(1/4) = 10 × (−0.602) ≈ −6 dB. For every decade of distance (×10), the drop is 20 × log₁₀(10) = −20 dB. The general formula: L₂ = L₁ − 20 × log₁₀(d₂ / d₁).

Note: this applies only in a free field (no reflections, no boundaries). In practice, ground reflection, barriers, and room acoustics all modify the actual attenuation.

Point source vs line source — when to use each model

A point source model applies when the source is small relative to the distance — a single machine, an HVAC exhaust, a compressor, or any source you can approximate as a dot in space. Sound energy radiates spherically, and doubling the distance gives −6 dB.

A line source model applies when the source is elongated compared to the observation distance — a busy highway, a rail line, a long conveyor, or a row of machines. Sound energy radiates cylindrically, and the active area grows linearly with distance (A = 2πrL), not as a square. This gives only −3 dB per doubling: L₂ = L₁ − 10 × log₁₀(d₂ / d₁).

Rule of thumb: if your observation point is closer to the source than the source is long, use a point source. As you move farther away (distance >> source length), the line source approximation becomes valid.

Point sources vs line sources vs plane sources

A point source radiates sound omnidirectionally in a sphere. Level drops by 6 dB per doubling of distance (inverse square law). Typical examples: a single machine, a compressor, a speaker, or a person talking in an open area.

A line source radiates sound cylindrically. Level drops by only 3 dB per doubling of distance because energy spreads over a cylindrical surface (area grows linearly with distance, not as a square). Typical examples: a busy road, a railway, a long conveyor belt, or a row of identical machines.

A plane source (large flat radiating surface) produces sound that does not attenuate with distance — level stays nearly constant until the observation point is far enough away that the source begins to look like a point. Typical examples: a large factory wall vibrating, a low-flying aircraft viewed from below, or a large piston. In practice, true plane sources are rare and bounded.

This calculator uses the point-source model (inverse square law, −6 dB/doubling) and the line-source model (−3 dB/doubling). Both are appropriate for isolated machinery or equipment in open air. For road traffic or railway noise, the line-source model is more realistic, and specialized methods such as FHWA TNM or ISO 9613-2 should be used for regulatory predictions.

Related tools: Noise Level Addition, TWA Noise Exposure Calculator, STEL Checker, and Air Changes Per Hour.

Real-world factors not captured by the formula

Ground reflection: hard surfaces such as asphalt, concrete, and water reflect sound and reduce the effective attenuation — levels near a hard ground can be up to 3 dB higher than free-field predictions. Soft ground (grass, soil, snow) absorbs sound and adds extra attenuation of 3–5 dB, especially at low frequencies and shallow (grazing) angles. ISO 9613-2 provides an explicit ground attenuation term (Agr) to account for this.

Atmospheric absorption: high-frequency components (above 1 kHz) attenuate faster than the inverse-square law predicts due to viscous and thermal losses in air. This effect becomes significant at distances beyond 100 m and is temperature- and humidity-dependent. ISO 9613-1 provides absorption coefficients (α, in dB/km) for different frequencies and atmospheric conditions.

Wind and temperature gradients: at night, temperature inversions and calm wind conditions can refract sound waves back toward the ground, causing noise to travel significantly farther than the formula predicts — up to 10–15 dB higher levels at long distances compared to daytime. Downwind propagation always exceeds upwind propagation. These effects are not captured by the simple geometric model.

Barriers and obstacles: walls, earth berms, and buildings block and diffract sound. A properly designed noise barrier can provide 10–20 dB of insertion loss in its shadow zone. These effects are not modeled here; use ISO 9613-2 or a full acoustic simulation tool (ray tracing, FDTD) for barrier design.

Directivity: many real noise sources are not omnidirectional. Exhaust stacks, fans, and speakers radiate more in one direction (described by a directivity index DI, in dB). The directional level can be 10 dB or more higher than the average level at the same distance in a preferred direction. The formula L₂ = L₁ − 20 × log₁₀(d₂/d₁) assumes an omnidirectional point source; if your source is directional, add the directivity correction before applying the distance attenuation.

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