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Acoustics
Add the sound levels of several sources, level reduction with distance and conversion between sound power and sound pressure.
Adding Sound Levels
energetic sum of up to 5 sources
Total level L_tot–
Increase over loudest source–
Rule of thumb: 2 equally loud sources → +3 dB · 10 equally loud sources → +10 dB.
Theory
Sound levels are logarithmic: you add the sound energies, not the dB values:Ltot = 10 · lg( Σ 10Lᵢ/10 )
- +3 dB = doubling of the sound energy
- +10 dB = 10 times the energy, perceived as "twice as loud"
- Sources more than 10 dB quieter contribute practically nothing
Level Reduction with Distance
point source or line source
Level reduction ΔL–
Level L₂ at r₂–
Free-field conditions: reflections, obstacles and air absorption are not considered. For comparison, TA Lärm (German noise regulation) limits for residential areas: 55 dB(A) by day, 40 dB(A) at night.
Theory
With spherical spreading, the sound energy is distributed over ever larger areas:Point source: L₂ = L₁ − 20 · lg r₂r₁
Line source: L₂ = L₁ − 10 · lg r₂r₁
- Point source: −6 dB per doubling of distance
- Line source: −3 dB per doubling of distance
- applies in the free field without ground or wall reflections
Sound Power ↔ Sound Pressure
sound pressure level at distance r
Measurement surface index–
Sound pressure level L_p–
Theory
The sound power level LW describes the source, the sound pressure level Lp what arrives at distance r:Lp = LW − 10 · lg 4·π·r²Q
- Q: directivity factor due to reflecting surfaces
- Machine on the floor: Q = 2 (hemispherical spreading)
- LW is given on nameplates and data sheets (e.g. fans)
Rough estimate for preliminary design. Permit procedures require a noise forecast according to TA Lärm (German noise regulation) / DIN ISO 9613-2.