Waves
Sound Level (Decibels)
Logarithmic scale for sound intensity.
Variables
βdB
Sound level
In decibels
IW/m²
Intensity
Sound intensity
In SI units: kg/s³
Allowed values: 0 or more
I₀W/m²
Reference intensity
10⁻¹² W/m²
In SI units: kg/s³
Allowed values: greater than 0
Derivation
β = 10 log₁₀(I/I₀) where I₀ = 10⁻¹² W/m².
Your notes
0/5000
Other waves formulas with the same quantities
- Intensity-Amplitude Relation (Wave Properties) shares Intensity
- Inverse Square Law (Intensity) (Wave Properties) shares Intensity
Where this formula is listed
- Waves formulas, under Sound Waves, alongside Speed of Sound in Gas, Beat Frequency, Mach Number, Shock Wave Angle (Mach Cone) and Sound Intensity Level Addition.
- In the waves list it comes after Speed of Sound in Gas and before Beat Frequency.
- 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 Level (Decibels) formula?
Sound Level (Decibels) is written β = 10 log₁₀(I/I₀). Logarithmic scale for sound intensity. It belongs to Waves, under Sound Waves.
What are the units in β = 10 log₁₀(I/I₀)?
In SI units, β is sound level, measured in dB; I is intensity, measured in kg/s³; I₀ is reference intensity, measured in kg/s³.
How is the Sound Level (Decibels) formula derived?
β = 10 log₁₀(I/I₀) where I₀ = 10⁻¹² W/m². The result is β = 10 log₁₀(I/I₀).