How do you add multiple noise sources together?

Sound pressure levels are added on an energy basis: L_combined = 10·log₁₀(Σ 10^(Li/10)) dB. For example, two 80 dB sources give 10·log₁₀(2×10⁸) ≈ 83 dB — not 160 dB. This is because SPL is a logarithmic measure of pressure squared (energy).

What is the difference between point source and line source attenuation?

A point source (e.g., a single machine) follows the inverse square law: SPL drops by 6 dB each time the distance doubles (−20·log₁₀(r/r₀)). A line source (e.g., a long road or pipeline) drops by 3 dB per doubling of distance (−10·log₁₀(r/r₀)). Real sources typically behave somewhere between the two depending on their geometry.

What is atmospheric absorption in acoustics?

Atmospheric absorption is the loss of acoustic energy as sound travels through air, caused by viscosity, heat conduction, and molecular relaxation. It increases strongly with frequency: roughly 1–4 dB/km at 1 kHz and 20–40 dB/km at 8 kHz (per ISO 9613-1). For low-frequency traffic noise it is negligible, but for machinery high harmonics at long distances it can be significant.

What does dBA mean and when is it used?

dBA (A-weighted sound pressure level) is SPL filtered through the A-weighting network, which mimics the frequency sensitivity of the human ear. It attenuates low and very high frequencies. Noise regulations worldwide — including occupational exposure limits (85 dBA 8-hour TWA) and environmental noise standards — universally specify dBA. Measured with a sound level meter on the 'A' weighting setting.

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Acoustics & Noise

Noise Level Calculator

Combine up to 5 noise sources, compute distance attenuation for point and line sources with atmospheric absorption, and apply A-weighting correction. SPL vs distance chart updates in real time.

A. Source Combination

Source 1dB

Source 2dB

Source 3dB

Source 4dB

Source 5dB

B. Distance Attenuation

Reference SPL L₀ at 1 m 80 dB

Source type

Evaluation distance r 50 m

Atmospheric absorption α 1.0 dB/km

Peak frequency 1000 Hz

Results

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Combined SPL [dB]

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SPL at distance r [dB]

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A-weighting corr. [dB]

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Level at r [dBA]

Formulas

Combine: $L_{sum}= 10\log_{10}\!\sum 10^{L_i/10}$
Point: $L(r)=L_0-20\log_{10}(r)-\alpha r/1000$
Line: $L(r)=L_0-10\log_{10}(r)-\alpha r/1000$
(reference $r_0=1$ m)

SPL vs Distance — Point vs Line Source Comparison

SPL Contribution per Source

What is Noise Level Combination?

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What exactly is the "combined noise level"? If I have two machines each making 80 dB of noise, is the total 160 dB?

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Basically, no! Sound pressure level (SPL) is a logarithmic measure of energy. You can't just add the decibels. In practice, you add the sound energies first, then convert back to decibels. For two 80 dB sources, the combined level is about 83 dB. Try it in the simulator above—add two sources with the same level and see how the total changes.

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Wait, really? So why does the formula have a 10*log10? And what's the difference between the "Point" and "Line" source options in the tool?

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Good questions! The 10*log10 comes from the definition of decibels for power or energy quantities. The key difference is in how sound spreads. A point source (like a pump) radiates sound spherically, so energy spreads over an area of $4\pi r^2$. A line source (like a busy road) radiates cylindrically, spreading over an area of $2\pi r L$. That's why the "distance attenuation" term changes from -20 log10(r) to -10 log10(r). Try switching the source type in the simulator and watch how the level drops off more slowly with distance for a line source.

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Okay, that makes sense. But what about the "Atmospheric absorption" slider? When does that matter, and what does the "Peak frequency" have to do with it?

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In practice, air isn't a perfect medium—it absorbs sound energy, especially at high frequencies. The absorption coefficient $\alpha$ (in dB/km) depends heavily on frequency and humidity. For instance, a 4000 Hz tone can be absorbed over 10 dB/km in dry air, while a 125 Hz tone might lose less than 1 dB/km. That's why you set a peak frequency. Move the "Evaluation distance" slider to a large value (like 500 m) and then adjust the "Atmospheric absorption"—you'll see it has a major impact on high-frequency noise over long distances.

Physical Model & Key Equations

The fundamental principle is the logarithmic addition of sound pressure levels from multiple incoherent sources, based on their energy.

$$L_{sum}= 10 \log_{10}\left( \sum_{i=1}^{n}10^{L_i/10}\right)$$

Where $L_{sum}$ is the total sound pressure level (dB), and $L_i$ is the level from the i-th source (dB). Each $L_i$ is calculated at the receiver point, accounting for distance and atmospheric loss.

For a single source, the level at a distance $r$ from the reference point ($r_0 = 1$ m) is calculated, with different models for geometric spreading.

$$L(r) = L_0 - 10 \cdot n \cdot \log_{10}\left(\frac{r}{r_0}\right) - \frac{\alpha r}{1000}$$

Here, $L_0$ is the reference SPL at 1 m (dB). $n$ is the attenuation exponent: $n=2$ for a point source (spherical spreading), $n=1$ for a line source (cylindrical spreading). $\alpha$ is the atmospheric absorption coefficient (dB/km), which is a function of the peak frequency and environmental conditions.

Real-World Applications

Environmental Impact Assessments: Before building a new factory or highway, engineers must predict the total noise impact on nearby communities. They model each noise source (compressors, fans, traffic lanes), calculate their contributions at different distances, and sum them to ensure legal limits are met.

Workplace Safety & Industrial Hygiene: In a manufacturing plant, a worker might be exposed to noise from multiple machines—lathes, conveyors, and air compressors. Calculating the combined 8-hour exposure level is critical for determining if hearing protection is required and if it meets OSHA or other regulatory standards.

Concert & Event Sound Planning: Sound engineers need to predict noise levels for audiences and, crucially, for the surrounding neighborhood to avoid noise complaints. They model each speaker array as a point source, account for distance, and sum their contributions to ensure front-row levels are safe and back-of-venue levels are adequate, while keeping spillover noise within limits.

Transportation Noise Modeling: Predicting noise from a railway or a busy road involves modeling it as a line source. Planners assess how noise diminishes with distance and use barriers or landscaping to mitigate it. The difference between point and line source attenuation is key here—road noise persists over much greater distances than a single vehicle's noise would.

Common Misconceptions and Points to Note

When starting with this tool, there are several pitfalls that beginners in CAE simulation often encounter. A major misconception is underestimating the importance of source type selection. For instance, are you inadvertently modeling the noise from a fan several meters long as a point source? If the physical size of the source is not sufficiently small compared to the distance to the prediction point (e.g., a 5m long source for a receiver 10m away), using a point source model will overestimate distance attenuation and calculate a lower noise level than in reality. As a rule of thumb, if the source size is more than about 1/5 of the evaluation distance, you should consider switching to a line or area source model.

Next is the mishandling of the "reference sound pressure L₀". This is the "noise level at a point 1 meter from the source," but it's risky to use catalog values directly without measured data. A difference of several decibels can arise depending on whether the catalog value is for "1 meter from the source surface" or "1 meter from the source center." For large machinery, this difference is not negligible. In practice, always check the metadata of the measurement conditions.

Finally, blind trust in the atmospheric absorption coefficient α. While the tool conveniently lets you set it with a slider, the actual α depends heavily on temperature, humidity, and frequency. The attenuation of high-frequency components differs completely between humid summer air at 80% and dry winter air. Rather than calculating all conditions with default values and considering them absolute, it's crucial to adopt an approach of sensitivity analysis—comparing results from multiple cases with varied parameters, understanding that "high-frequency sounds travel farther in dry winter conditions with low humidity."

Related Engineering Fields

The physical models behind this noise level calculation tool are actually closely linked to various engineering fields beyond noise prediction. First and foremost is radio wave propagation engineering. Sound waves and radio waves share the commonality of being waves; the distance attenuation from a point source (the $1/r^2$ law) is mathematically isomorphic to free-space path loss in radio waves. This connects to concepts used in antenna design and wireless communication link budget calculations.

Next is vibration engineering, particularly the prediction of sound radiated from structures. The process by which vibrations from plates or machine enclosures radiate into the air as sound is evaluated as "acoustic radiation efficiency," and it is this tool's calculation part that handles the propagation of the ultimately radiated sound. Conversely, the same concepts used for contribution analysis of multiple noise sources can be applied to source identification (determining which vibration modes are the primary noise sources).

Furthermore, the connection with fluid engineering should not be overlooked. For phenomena where the fluid itself is the noise source, such as aerodynamic noise or jet noise, results from CFD (Computational Fluid Dynamics) simulations are sometimes used as input for estimating source strength. In other words, this tool can serve as part of a multiphysics coupling process, where $L_0$ is estimated from vortex strength or fluctuating pressure obtained via CFD, and then the tool calculates propagation to distant locations.

For Further Learning

Once you're comfortable with this tool's calculations and want to know more about "why it works that way," it's time to take the next step. The first area to tackle is "the fundamental mathematics of acoustics." The core lies in "decibel calculations" and "fundamental solutions to the wave equation." For decibel calculations, mastering quick estimation methods for energy summation ($10\log_{10}(10^{L_1/10}+10^{L_2/10})$) without using log tables or slide rules (e.g., if the difference between two levels is 3dB, the sum is approximately +1.8dB) is practically useful.

Next, learn the background of the "atmospheric absorption coefficient α," which is treated as a black box in the tool. This is one of the achievements of classical acoustics, comprising three main mechanisms: viscous losses in air, thermal conduction losses, and molecular relaxation (vibrational energy exchange between oxygen and nitrogen molecules). The International Organization for Standardization (ISO) standard (ISO 9613-1) specifies empirical formulas for determining α from temperature, humidity, and frequency. Implementing these yourself will deepen your understanding.

The ultimate learning goal is to understand the connection to "geometrical acoustics" and "wave-based acoustic FEM/BEM." This tool assumes "free field" direct sound propagation, but real environments involve ground reflections, diffraction by buildings, and refraction due to wind and temperature gradients. The next step is to learn about more advanced, higher-accuracy prediction methods and their limitations—such as the "image source method" for considering reflections, the "ray tracing method" for complex terrain, and "Finite Element Method (FEM)" or "Boundary Element Method (BEM)" for enclosed spaces or low frequencies. This knowledge is the path to becoming a true CAE engineer.