Quick answer Sound pressure level is L = 20·log₁₀(p/p₀) dB SPL, referenced to p₀ = 20 μPa, the threshold of hearing. A point source falls off as ΔL = 20·log₁₀(r₀/r), about 6 dB per doubling of distance, and n identical sources add as L_n = L + 10·log₁₀(n) — roughly +3 dB for two.
Set a reference sound level, source distance and number of sources to compute SPL, distance attenuation and combined level. Compare with everyday reference sounds.
Parameters
Sound-source preset
Sound pressure level L
dB
04080120140
Reference distance r₀
m
Calculation distance r
m
Number of identical sound sources n
While paused, moving a slider updates the results immediately.
Results
—
Combined SPL [dB]
—
Number of Sources n
—
Per Source [dB]
—
Increase Due to Addition [dB]
Combining equally intense sources follows the logarithmic law \(L_\text{total}=10\log_{10}\!\sum_i 10^{L_i/10}\). Example: two 60 dB sources → 63 dB (+3 dB); ten → 70 dB (+10 dB).
Scale
Sound pressure p
0.356
Pa
Level at distance r
65.0
dB @ r
n sources combined
85.0
dB
Sound intensity I
3.16e-4
W/m²
Dist
Sum
Theory & Key Formulas
Environment/source
dB SPL
Sound-pressure ratio (p/p₀)
🌿 Rustling leaves
20 dB
10×
📚 Quiet library
30 dB
31×
🗣️ Normal conversation (1 m)
60 dB
1,000×
🔨 Construction site
85 dB
17,783×
🚂 Passing train (10 m)
90 dB
31,623×
🔊 Live concert
110 dB
316,228×
🚀 Jet takeoff (25 m)
130 dB
3.16×10⁶×
Theory & Key Formulas
\(L = 20\log_{10}\!\left(\frac{p}{p_0}\right)\) dB SPL
\(p_0 = 20\,\mu\text{Pa}\) (threshold of hearing)
Distance attenuation: \(\Delta L = 20\log_{10}(r_0/r)\) dB
Combined level of n sources: \(L_n = L + 10\log_{10}(n)\)
FAQ
What is a decibel?
A decibel is a logarithmic unit expressing the ratio of sound pressure to a reference value. The logarithmic scale matches human hearing sensitivity.
Why does doubling distance reduce level by 6 dB?
A point source spreads as a spherical wave; doubling distance quadruples the area, cutting intensity to 1/4. 10*log10(0.25) = -6 dB.
At what dB does hearing become risky?
Exposure to 85 dB+ for extended periods risks hearing loss. 110-120 dB+ can cause damage even briefly.
Is 0 dB complete silence?
No. 0 dB is the reference threshold of hearing (20 microPascal). Negative dB values are also possible for very quiet sounds.
🙋
I can see the simulation updating, but what exactly is being calculated here?
🎓
Great question! The simulator solves the governing equations in real time as you move the sliders. Each parameter you control directly affects the physical outcome you see in the graph. The key is to build an intuitive feel for how each variable influences the result — that's how engineers develop physical judgment.
🙋
So when I increase this parameter, the curve shifts significantly. Is that a linear relationship?
🎓
It depends on the model. Some relationships are linear, but many engineering phenomena are nonlinear. Try moving the sliders to extreme values and see if the output changes proportionally — if the graph shape changes, that's a sign of nonlinearity. This hands-on exploration is exactly what simulations are best for.
🙋
Where is this kind of analysis actually used in practice?
🎓
Constantly! Engineers run these calculations during the design phase to quickly screen parameters before investing in expensive physical tests or detailed finite element simulations. Getting comfortable with these simplified models is a real engineering skill.
Set the reference sound pressure level (db-slider) using the decibel scale, typically 94 dB for a 1 Pa reference at 1 meter.
Enter the reference distance (r0-slider) in meters where the initial SPL was measured—commonly 1 m for machinery noise.
Input your desired calculation distance (r-slider) in meters to predict sound level attenuation per inverse square law.
Adjust the geometric spreading exponent (n-slider) between 2 (point source, free field) and 1 (line source, semi-diffuse field) to match your acoustic environment.
Worked Example
A pneumatic impact hammer generates 104 dB SPL at r0=1 m in a factory. Calculate SPL at r=10 m with n=2 (free-field outdoor conditions): SPL(10m) = 104 - 20*log10(10/1)*2 = 104 - 40 = 64 dB. For indoor reverberant spaces with n=1.5: SPL(10m) = 104 - 30 = 74 dB, showing how room acoustics increase attenuation inefficiency.
Practical Notes
Use n=2 for outdoor point sources (compressors, HVAC units); use n=1 for ductwork or highway traffic treated as line sources.
Add 3-5 dB correction for industrial reverberant rooms where absorption coefficient ≤0.2 (concrete walls, metal cladding).
Monitor hearing protection requirements when field SPL exceeds 85 dB; OSHA mandates controls above 90 dB.
Validate measurements at reference distance with Class 2 sound level meter per ISO 3744 before running decay predictions.