Sound Level Distance Attenuation Calculator
Determine noise level reduction over distance using the acoustic inverse square law for point sources (chillers, pumps, fans) and line sources (traffic roads).
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Sound Propagation Physics & The Inverse Square Law
As acoustic waves radiate outward from a noise source into an unobstructed open environment, the acoustic sound power distributes over a rapidly expanding geometric surface area. Because sound intensity is energy per unit area, decibel sound pressure levels diminish predictably with distance according to the Inverse Square Law.
Governing Geometric Propagation Formulas
- Point Source (Spherical / Hemispherical Spreading):
For isolated equipment (chillers, air compressors, rooftop fans, generators) where source dimensions are small relative to distance:Lp2 = Lp1 - 20 × log10(r2 / r1)
Every doubling of distance (2×) reduces sound pressure level by exactly 6.02 dB. - Line Source (Cylindrical Spreading):
For continuous linear noise sources (congested highways, long outdoor piping mains, train corridors):Lp2 = Lp1 - 10 × log10(r2 / r1)
Every doubling of distance reduces sound pressure level by only 3.01 dB. - Subjective Human Perception Rule of Thumb:
- -3 dB drop: Barely noticeable change to human hearing
- -5 dB drop: Readily noticeable reduction in loudness
- -10 dB drop: Perceived subjectively as half as loud (50% reduction)
- -20 dB drop: Perceived as 75% quieter (1/4 as loud)
Frequently Asked Questions
Why does doubling the distance not cut decibels in half?
The decibel (dB) scale is logarithmic, not linear. A 10 dB reduction represents a 90% reduction in actual acoustic sound energy, which the human ear and brain interpret subjectively as cutting loudness in half. If 80 dB was cut in half linearly to 40 dB, it would represent a 10,000-fold reduction in sound intensity.
How does atmospheric weather affect sound propagation?
Sound travels farther downwind because wind shear bends sound waves downward toward the ground. Conversely, upwind propagation refracts sound waves upward into the sky, creating an acoustic shadow zone near the ground. Temperature inversions at night also trap and refract sound waves downward over surprising distances.
What is typical municipal property line noise limit?
Most North American city noise ordinances enforce a daytime property boundary limit of 60 to 65 dBA, and a nighttime limit of 50 to 55 dBA in residential zones.
What is the difference between Sound Power (Lw) and Sound Pressure (Lp)?
Sound Power (Lw) is the total acoustic energy generated by the machine per second—like the wattage rating of a light bulb. Sound Pressure (Lp) is what a sound level meter measures at a specific distance—like the foot-candles of light illuminating a table.