Introduction to Decibels

What is a dB?

The intensity of a sound wave is the average amount of energy transmitted per unit time through a unit area in a specified direction. The amount of energy per unit time is power, and intensity is therefore the amount of power transmitted through a unit area in a specified direction. Power is measured in watts, and intensity is therefore measured in watts per square meter. Scientists often specify sound intensity as a ratio, however. The sound intensity level, I, in decibels is defined as 10 times the logarithm of the ratio of the intensity of a sound wave to a reference intensity:

$I(db) = 10 log_{10} \left ( \frac{I_{Sound}}{I_{Reference}} \right )$

The unit for intensity is the bel, named in honor of Alexander Graham Bell, the inventor of the telephone. This unit is seldom used, however, because the human ear is very sensitive. Humans can detect changes of as little as 1/10 of a bel, that is, a decibel. For that reason, sound intensity levels are defined in decibels (written as dB). The decibel is a relative unit, not an absolute one.

Acoustic intensity is rarely measured directly, however. Underwater microphones, called hydrophones, measure the pressure (amplitude) of a sound wave rather than its intensity. Because the intensity of a sound wave is proportional to the square of its pressure p:

$I = \left ( \frac{p^2}{\rho c} \right )$

(“ρ” is the density of medium carrying the sound and c is the speed of sound), the sound pressure level in dB can be computed directly from the measured pressure:

$I(db) = 10 log_{10} \left ( \frac{p^2_{Sound}}{p^2_{Reference}} \right ) = 20log_{10} \left ( \frac{p_{Sound}}{p_{Reference}} \right )$

Sound pressure level will usually be shortened to “sound level” on the DOSITS website, unless confusion could result.

To be able to compare sound levels given in dB to one another, a standard reference intensity or reference pressure must always be used. It is therefore essential that sound levels expressed in decibels include the reference pressure. Scientists have arbitrarily agreed to use the intensity of a sound wave with a pressure of 1 microPascal (µPa) as the reference intensity for underwater sound. In air, however, scientists have agreed to use the intensity of a sound wave with a higher pressure of 20 microPascals as the reference intensity. Sound levels given in dB in water are therefore not the same as sound levels given in dB in air. To make it clear for the reader, this website will use “underwater dB” for underwater sounds.

The logarithmic nature of the dB scale means that each 10 dB increase is a ten-fold increase in acoustic power. A 20-dB increase is then a 100-fold increase in power, and a 30-dB increase is a 1000-fold increase in power. A ten-fold increase in acoustic power does not mean that the sound is perceived as being ten times louder, however. Humans perceive a 10 dB increase in sound level as only a doubling of sound loudness, and a 10 dB decrease in sound level as a halving of sound loudness.