CALCULATOR 03

Decibel Attenuation & Inverse-Square Modeler

RADIATION: SPHERICAL / SEMI-REVERBERANT

Distance Decay Parameters

Reference Distance ($d_1$):

meters

Sound Level at $d_1$ ($L_1$):

dB SPL

Target Distance ($d_2$):

meters

Acoustic Environment Model:

Decibel Summation (Adding Incoherent Sources):

TOTAL COMBINED SPL: 88.0 dB SPL

Decay Calculations

SOUND LEVEL AT TARGET ($L_2$): 71.9 dB SPL

ACOUSTIC DECIBEL ATTENUATION: -18.1 dB

OSHA & NIOSH Permissible Noise Exposure Limits:

Sound Level	NIOSH Limit	Perception
85 dB SPL	8 Hours	Heavy Traffic / Studio Mon.
88 dB SPL	4 Hours	Loud Classical Concert
91 dB SPL	2 Hours	Gas Lawnmower
100 dB SPL	15 Minutes	Nightclub / Live Drums
110 dB SPL	< 1 Minute	Rock Concert / PA System

The Inverse-Square Law in Architectural Acoustics

In a free acoustic field (an open space without reflective walls or ceilings), sound radiates outward spherically from an omnidirectional point source. Because the surface area of a sphere increases proportionally with the square of the radius ($A = 4\pi r^2$), the acoustic sound intensity spread over the sphere drops by a factor of four each time the distance doubles.

$$\Delta L = 20 imes \log_{10}\left(rac{d_1}{d_2} ight) ext{ dB}$$

The Inverse-Square Law decibel attenuation formula for sound pressure level (SPL)

Because human hearing perceives loudness logarithmically, a fourfold drop in physical sound energy translates to an exact -6.02 dB attenuation for every doubling of distance (e.g. from 1m to 2m, or 2m to 4m).