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Sound Intensity Level Addition

βtotal=10log⁡10(∑10βi/10)\beta_{total} = 10\log_{10}\left(\sum 10^{\beta_i/10}\right)

How to add multiple sound sources in decibels (cannot simply add dB values).

Variables

β_total
Total sound level
Combined intensity level
dB
βᵢ
Individual sound levels
Each source in dB
dB

Derivation

Convert each dB to intensity: I = I₀·10^(β/10), sum intensities, convert back to dB.

Your notes

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Common questions

What is the Sound Intensity Level Addition formula?

Sound Intensity Level Addition is written βₜₒₜₐₗ = 10log₁₀(Σ10βᵢ/¹⁰). How to add multiple sound sources in decibels (cannot simply add dB values). It belongs to Waves, under Sound Waves.

What are the units in βₜₒₜₐₗ = 10log₁₀(Σ10βᵢ/¹⁰)?

In SI units, β_total is total sound level, measured in dB; βᵢ is individual sound levels, measured in dB.

How is the Sound Intensity Level Addition formula derived?

Convert each dB to intensity: I = I₀·10^(β/10), sum intensities, convert back to dB. The result is βₜₒₜₐₗ = 10log₁₀(Σ10βᵢ/¹⁰).