Distance Attenuation Calculator
Calculate how sound pressure level changes with distance using the inverse square law
Calculate Sound Attenuation
Distance from sound source to reference point
Distance from sound source to target point
Sound pressure level at reference point
Attenuation Calculation Results
Formulas used:
SPL₂ = SPL₁ - 20 × log₁₀(R₂/R₁)
Distance ratio: 0.00× | Intensity ratio: 0.000×
Inverse Square Law Analysis
Example Calculation
Highway Noise Attenuation
Scenario: Sound from highway to two houses at different distances
Distance 1 (near house): 50 m from highway
Distance 2 (far house): 200 m from highway
SPL at near house: 75 dB
Application: Environmental noise assessment, urban planning
Calculation
SPL₂ = SPL₁ - 20 × log₁₀(R₂/R₁)
SPL₂ = 75 - 20 × log₁₀(200/50)
SPL₂ = 75 - 20 × log₁₀(4)
SPL₂ = 75 - 20 × 0.602
SPL₂ = 75 - 12.04
SPL₂ = 62.96 dB
Result: The far house experiences 12 dB less noise than the near house.
Distance Effects
Attenuation Facts
Sound follows the inverse square law in free field conditions
6 dB reduction for every doubling of distance
20 dB reduction = 10× distance increase
Intensity decreases with distance squared
Real environments may have additional absorption
Understanding Distance Attenuation and the Inverse Square Law
What is Distance Attenuation?
Distance attenuation describes how sound pressure level decreases as you move farther from the source. This occurs because the same acoustic energy spreads over a larger area as the distance increases, reducing the intensity at any given point.
The Inverse Square Law
- •Sound intensity is inversely proportional to distance squared
- •Double the distance = quarter the intensity
- •Each doubling of distance reduces SPL by 6 dB
- •Applies to point sources in free field conditions
Attenuation Formula
SPL₂ = SPL₁ - 20 × log₁₀(R₂/R₁)
Sound pressure level attenuation
I₂ = I₁ × (R₁/R₂)²
Intensity inverse square relationship
SPL₁, SPL₂: Sound pressure levels at points 1 and 2
R₁, R₂: Distances from source to points 1 and 2
I₁, I₂: Sound intensities at points 1 and 2
Factor 20: Converts amplitude ratio to dB
Practical Rules of Thumb
6 dB Rule
Distance doubles → 6 dB reduction
20 dB Rule
Distance 10× → 20 dB reduction
Intensity Rule
Distance 2× → Intensity ÷4
These rules apply in free field conditions with no obstacles, reflections, or additional absorption. Real-world environments may have additional attenuation due to air absorption, ground effects, barriers, and atmospheric conditions.
Applications and Uses
Environmental Acoustics
Noise impact assessments, urban planning, highway noise prediction, and residential area sound level calculations.
Audio Engineering
Concert hall acoustics, speaker placement, recording studio design, and sound system coverage calculations.
Industrial Safety
Workplace noise exposure assessment, machinery noise control, and hearing protection zone determination.