Distance Attenuation Calculator

Sound spreads out as it travels, so its level falls with distance.

How the Math Works

The formula L₂ = L₁ − 20·log₁₀(d₂ ÷ d₁) calculates sound level attenuation with distance based on the inverse-square law. Here, L₁ is the original sound level at distance d₁, and L₂ is the reduced level at distance d₂. The logarithm term quantifies how much the sound diminishes as it spreads over a larger area. Doubling the distance (d₂ = 2·d₁) reduces the level by approximately 6 dB, since 20·log₁₀(2) ≈ 6. This reflects how sound energy disperses over a sphere's surface area, which grows with the square of distance, hence the logarithmic relationship.

Practical Applications

To use this calculator, input the initial sound level (L₁) and its source distance (d₁), then specify a new distance (d₂) to find the expected level (L₂). Engineers apply this in acoustical design, such as placing loudspeakers at optimal distances for even coverage or determining safe noise exposure limits. For example, if a speaker emits 90 dB at 1 meter, moving 10 meters away reduces the level to 70 dB (90 − 20·log₁₀(10) = 70 dB), helping to plan sound systems or noise barriers effectively.

Day-to-Day Use

This calculation helps everyday sound management, like adjusting home speaker placement to avoid distortion or ensuring audio clarity in events. It also explains why traffic noise fades as you move away from roads, or why sirens and construction sounds become quieter at a distance. By predicting sound decay, you can better manage noise pollution, select quieter zones for outdoor activities, or gauge how far emergency alerts can be heard safely.

Worked example

90 dB at 1 m → 70 dB at 10 m.

FAQ