Sound Intensity Level Addition

\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

βᵢ

Individual sound levels

Each source in dB

Derivation

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

Your notes

0/5000

Where this formula is listed

Waves formulas, under Sound Waves, alongside Speed of Sound in Gas, Beat Frequency, Mach Number and Shock Wave Angle (Mach Cone).
In the waves list it comes after Shock Wave Angle (Mach Cone) and before Doppler Effect (General).
Waves formula sheet, one of 37 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Sound Intensity Level Addition formula?

Sound Intensity Level Addition is written β_total = 10 log₁₀(Σ10^(β_i/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 β_total = 10 log₁₀(Σ10^(β_i/10))?

In SI units, β_t otal 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 β_total = 10 log₁₀(Σ10^(β_i/10)).