ISO 9613-2 based SPL vs distance for point and line sources, with atmospheric absorption, Maekawa barrier insertion loss, and ground effect.
Parameters
Source Type
SPL at 1 m reference
dB
Target distance r
m
Frequency band
Center frequency: 500 Hz
Atmospheric Conditions
Temperature T
°C
Relative Humidity RH
%
Ground type
Noise Barrier
Barrier height H
m
Source-barrier dist d_s
m
SPL vs Distance
Results
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SPL at r (dB)
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Geometric (dB)
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Atm. Absorb (dB)
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Barrier IL (dB)
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Ground Effect (dB)
Att
Engineering Note
ISO 9613-2 is the industry standard for source power level → receiver SPL prediction. CNOSSOS-EU is required for European Environmental Noise Directives. For complex geometries and room acoustics, FEM/BEM numerical acoustics solvers provide much higher fidelity.
Atmospheric absorption (ISO 9613-1): $A_{atm}= \alpha \cdot r / 1000$ [dB]
Maekawa barrier: $IL = 10\log_{10}(3 + 20N),\quad N = 2\delta/\lambda$
What is Noise Propagation & Distance Attenuation?
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What exactly is "distance attenuation"? I know sound gets quieter as you move away, but is there a simple rule for how much?
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Basically, it's the rate at which sound energy spreads out and weakens. For a simple point source, like a single speaker in an open field, the sound pressure level drops by about 6 decibels every time you double the distance. Try moving the "Target distance r" slider in the simulator above and watch the SPL drop.
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Wait, really? But the simulator has a "Line source" option too. Does that follow the same 6 dB rule?
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Good catch! No, it doesn't. A line source, like a long, busy highway or a pipeline, behaves differently. Because the sound is emanating from a line, it only spreads out in a cylinder, not a sphere. So it attenuates slower—only about 3 dB per distance doubling. Switch the "Source Type" in the tool and you'll see the calculated SPL stays higher at longer distances.
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So the basic formulas don't account for weather or barriers? What's the point of all the other parameters like humidity and barrier height?
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Exactly right! The simple formulas are for a perfect, free field. In practice, air absorbs sound (especially high frequencies), the ground can reflect or absorb it, and barriers block it. That's why we use the ISO 9613-2 standard. For instance, try setting a high "Frequency band" and then increase the "Temperature T". You'll see the atmospheric absorption loss change. Adding a "Barrier height H" will introduce a significant diffraction loss, which is crucial for predicting noise behind a wall.
Physical Model & Key Equations
The core of the calculation is geometric spreading from the source. For an omnidirectional point source, sound energy spreads over the surface area of a sphere ($4\pi r^2$), leading to an inverse square law for sound pressure.
$$L_p(r) = L_W - 20\log_{10}(r) - 11$$
Where $L_p(r)$ is the sound pressure level (dB) at distance $r$ (m), and $L_W$ is the sound power level (dB) of the source. The $-20\log_{10}(r)$ term represents the 6 dB per doubling rule.
For an infinitely long line source, sound spreads over the surface area of a cylinder ($2\pi r$ per unit length), leading to different attenuation.
$$L_p(r) = L_W' - 10\log_{10}(r) - 8$$
Here, $L_W'$ is the sound power level per meter of line source (dB/m). The $-10\log_{10}(r)$ term gives the 3 dB per doubling rule. The ISO 9613-2 standard adds correction terms ($A_{atm}+ A_{gr}+ A_{bar}$) to these equations for atmospheric, ground, and barrier effects, which the simulator calculates based on your input parameters.
Frequently Asked Questions
Point sound sources are used when sound radiates from a single point, such as a factory exhaust vent or a single machine. Line sound sources are applied to continuous linear sound sources, such as a line of vehicles on a road or factory piping. For point sound sources, the sound attenuates by approximately 6 dB when the distance doubles, whereas for line sound sources, the attenuation is approximately 3 dB.
Atmospheric absorption causes greater attenuation at higher frequencies, and becomes non-negligible especially for sounds above 500 Hz or when the propagation distance exceeds several hundred meters. If the input values for temperature and humidity differ from actual measurements, errors may occur, so please set local weather data as accurately as possible during calculation.
Based on ISO 9613-2, the attenuation is calculated from the diffraction path difference of the sound barrier relative to the straight line connecting the sound source and the receiver point. Since the results are updated in real time when the height or position of the barrier is changed, this can be used to study optimal sound barrier designs.
The graphs visualize the sound pressure level attenuation curve over distance, making them useful for predicting noise at site boundaries and comparing the effects of countermeasures. Additionally, by overlaying multiple conditions, you can intuitively evaluate differences such as the presence or absence of a sound barrier or the type of sound source.
Real-World Applications
Environmental Noise Mapping: This is the primary application of ISO 9613-2. City planners and environmental agencies use these calculations to create noise maps for roads (line sources), industrial plants (point sources), and railways. These maps are often required by law, like the EU's Environmental Noise Directive, to assess population exposure.
Industrial Noise Control: When designing a factory or a power plant, engineers must predict noise levels at the site boundary to comply with regulations. They use these models to determine if barriers are needed, how high they should be, and what ground treatment (e.g., grass vs. asphalt) would help reduce propagation.
Transportation Infrastructure Planning: Before building a new highway or expanding an airport, engineers model noise propagation to evaluate the impact on nearby communities. The line source model is critical for highways, while point source models apply to stationary sources like ventilation shafts or transformer stations.
Workplace Safety & Site Planning: On construction sites or in mining, predicting how noise from heavy machinery (a point source) propagates helps in planning operator positions and setting up mandatory hearing protection zones. The atmospheric absorption settings are key for high-frequency tool noise.
Common Misunderstandings and Points to Note
When you start using this type of simulation, there are a few common pitfalls. First is "How to choose sound sources". In factory noise prediction, are you inputting all machinery as a single "point source"? For example, if multiple pumps and fans are spread across a wide site, modeling them as a single point source lumped in one location can significantly skew predictions at close distances. The correct approach is to place major sound sources as individual point sources and evaluate their combined sound. Remember that the tool can only calculate one source type at a time, so when dealing with multiple sources, you need to sum the results acoustically by energy.
Next is "Over-reliance on default parameters". Parameters for "ground effect" require particular caution. The tool offers broad classifications like "soft ground" or "mixed ground", but real sites are complex—asphalt next to grass, then farmland, etc. Uniformly selecting "soft ground" tends to overestimate attenuation, especially at medium distances (50-200m). If you have actual measurement data, it's crucial to fine-tune parameters accordingly.
Finally, "Taking simulation results as absolute truth". While ISO 9613-2 is a standard methodology, it remains a "prediction model". For instance, the Maekawa formula used in barrier calculations assumes an infinitely long wall. Actual walls have edges, and the "edge effect" where sound diffracts around them is not considered. It's common for a calculation to show a 20 dB reduction, while on-site measurements near the edge show only 10 dB. Think of the simulation as a tool to "understand trends and relatively compare the effectiveness of countermeasures".