| Basic Principle | Sound level decreases with distance due to energy spreading and absorption |
| Decibel (dB) | Logarithmic unit used to express the ratio of two values of a physical quantity |
| Kilometer (km) | Unit of distance equal to 1000 meters |
| Point Source Formula | Distance (km) = 10^(dB / 20) |
| Line Source Formula | Distance (km) = 10^(dB / 10) |
| Inverse Square Law | Sound intensity decreases proportionally to the square of the distance from the source |
| 6 dB Rule (Point Source) | Sound level decreases by 6 dB for each doubling of distance |
| 3 dB Rule (Line Source) | Sound level decreases by 3 dB for each doubling of distance |
| Point Source Examples | Individual machinery, speakers, point explosions |
| Line Source Examples | Highways, railways, pipelines |
| Free Field Conditions | Assumes no reflections or obstructions |
| Atmospheric Absorption | Additional attenuation, especially at high frequencies and large distances |
| Ground Effect | Can cause additional attenuation or enhancement |
| Temperature Effects | Can alter sound propagation paths |
| Wind Effects | Can increase or decrease effective propagation distance |
| Humidity Effects | Affects atmospheric absorption, especially at high frequencies |
| Frequency Dependence | Higher frequencies generally attenuate more with distance |
| Near Field vs Far Field | Formulas apply in far field; near field may have different behavior |
| Barriers and Obstacles | Can provide additional noise reduction |
| Practical Applications | Environmental noise assessment, urban planning, concert sound design |
| Limitations | Real-world conditions may cause deviations from theoretical predictions |
| Combined Sources | Total SPL is logarithmic sum of individual source contributions |
| Directivity Factor | Accounts for non-uniform radiation patterns of real sources |
| Reference Distance | Typically 1 meter for point sources, 15 meters for line sources |
| SPL Calculation | SPL2 = SPL1 – 20 × log10(d2/d1) for point sources |
| SPL2 = SPL1 – 10 × log10(d2/d1) for line sources |
| Perception of Loudness | 10 dB reduction perceived as approximately half as loud |
| Typical Outdoor Ranges | From 0 dB (threshold of hearing) to 140 dB (jet engine at close range) |
| Safety Considerations | Prolonged exposure to levels above 85 dB can cause hearing damage |
| Measurement Equipment | Sound level meters, often with A-weighting for human ear response |
| Standards | ISO 9613-2 for outdoor sound propagation |
| Software Tools | Various acoustic modeling software available for complex scenarios |