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How is sound intensity measured in decibels?

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Diagram showing auditory mechanisms in insects, including labeled illustrations of a scolophore organ, the mosquito ear with antenna shaft and scolophores, the cicada ear with auditory capsule and tympanic membrane, and the grasshopper ear with sensory body and tympanic membrane. — sound reception Auditory mechanisms in insects. (Left) A scolophore organ. (Top right) The mosquito ear. (Centre right) The ear of the cicada *Magicicada septendecim*. (Bottom right) The ear of the grasshopper.

The decibel (dB) is a unit used to express the relative intensity of sound on a logarithmic scale, which is necessary because the human ear responds to sound intensity in a nonlinear fashion.123

Because the ear can detect an enormous range of sound pressures—from the threshold of hearing to the threshold of pain—a logarithmic scale is more practical than a linear one. The intensity of a sound in decibels is defined by the following formula:13

$L = 10 \log_{10} (\frac{I}{I_{0}})$

In this equation:
* $L$ represents the sound intensity level in decibels.1
* $I$ is the intensity of the sound wave being measured, typically in watts per square metre.1
* $I_{0}$ is the reference intensity, set at the threshold of hearing (approximately $10^{- 12}$ watt per square metre at 1,000 hertz).142

On this scale, each unit of increase corresponds to a constant multiplicative factor in absolute intensity. A 10-decibel increase represents a tenfold increase in intensity, while a 20-decibel increase represents a 100-fold increase. One decibel is generally considered the smallest difference in loudness detectable by the human ear.1543