Acoustics and physics
Inverse-square law
Also known as 1/r² law (acoustic), geometric spreading.
The inverse-square law states that the intensity of a point-source sound wave falls as 1/r² with distance. Expressed in decibels, SPL decreases by approximately 6 dB for every doubling of distance from the source in a free field.
Worked example for a sonic horn
A horn rated at 150 dB SPL at 1 m on the bell axis will produce, in free-field conditions:
| Distance | Approximate SPL |
|---|---|
| 1 m | 150 dB |
| 2 m | 144 dB |
| 4 m | 138 dB |
| 8 m | 132 dB |
| 16 m | 126 dB |
Where the rule breaks down
Three real conditions modify the textbook result. Inside a vessel, reflections from walls and tube banks reinforce the sound field and slow the fall-off; geometry no longer behaves as a free field. In the near field of the bell, the simple 1/r² rule does not apply. And at long distances and high frequencies, attenuation absorbs additional energy beyond geometric spreading.
Why it matters for noise exposure
Worker exposure assessments work backwards from the inverse-square law: knowing the nameplate SPL and the operator-station distance, the predicted exposure can be compared with OSHA 29 CFR 1910.95 or EU Directive 2003/10/EC action levels.
Related terms
Related terms
- Sound pressure levelSPL is the logarithmic measure of sound pressure in decibels relative to a 20 µPa reference. Industrial sonic horns operate at 140–180 dB SPL.
- Attenuation (acoustic)Attenuation is the loss of acoustic energy as a sound wave propagates. Higher frequencies attenuate faster, which is why low-frequency sonic horns reach further in industrial vessels.
- Near field and far fieldThe near field is the complex acoustic zone within roughly one wavelength of the source. The far field is the simpler region beyond, where the inverse-square law applies.