---
title: "Inverse-square law"
description: "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."
canonical_url: "https://sylio.co/glossary/inverse-square-law"
last_updated: "2026-06-28T02:29:23.111Z"
---

The **inverse-square law** states that the intensity of a point-source sound wave falls as 1/r² with distance. Expressed in [decibels](/glossary/decibel), [SPL](/glossary/sound-pressure-level) 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:

<table>
<thead>
  <tr>
    <th>
      Distance
    </th>
    
    <th>
      Approximate SPL
    </th>
  </tr>
</thead>

<tbody>
  <tr>
    <td>
      1 m
    </td>
    
    <td>
      150 dB
    </td>
  </tr>
  
  <tr>
    <td>
      2 m
    </td>
    
    <td>
      144 dB
    </td>
  </tr>
  
  <tr>
    <td>
      4 m
    </td>
    
    <td>
      138 dB
    </td>
  </tr>
  
  <tr>
    <td>
      8 m
    </td>
    
    <td>
      132 dB
    </td>
  </tr>
  
  <tr>
    <td>
      16 m
    </td>
    
    <td>
      126 dB
    </td>
  </tr>
</tbody>
</table>

## 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](/glossary/near-field-far-field) of the bell, the simple 1/r² rule does not apply. And at long distances and high frequencies, [attenuation](/glossary/attenuation-acoustic) 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](/glossary/osha-29-cfr-1910-95) or [EU Directive 2003/10/EC](/glossary/eu-directive-2003-10-ec) action levels.

## Related terms

- [Sound pressure level](/glossary/sound-pressure-level)
- [Attenuation (acoustic)](/glossary/attenuation-acoustic)
- [Near field / far field](/glossary/near-field-far-field)