# Decibel

Last revised by Jeremy Jones on 13 Mar 2024

The decibel (dB) is a unit that measures the relative difference between two sound intensities. The relationship is logarithmic:

###### dB = 10 log (I2 / I1)
• dB = relative intensity of the sounds

• I1 = intensity of sound 1

• I2 = intensity of sound 2

Informally, decibel is a unit of "loudness", which is an informal way of expressing the intensity of sound, which strictly speaking represents the energy it deposits per unit time. This, in turn, is related to the square of the pressure the sound wave physically exerts (in N/m2).

• (sound intensity) is proportional to (the sound's pressure)2

• (I) is proportional to (P)2

Thus, ultimately, the decibel is a relative gauge of different sound pressures.

Medical ultrasound uses units of intensity of milliwatts per centimeter2 (mW/cm2), but the decibel is a pure number since it is the logarithmic ratio of the two intensities.

The decibel's logarithmic relationship allows large ranges of sound intensity to be handled in more manageable units:

• 10x rise in sound intensity corresponds to a 10 dB increase

• 100x rise in sound intensity corresponds to a 20 dB increase

• 1000x rise in sound intensity corresponds to a 30 dB increase

...and so on. This is useful in medical ultrasound since the difference in intensity between a transmitted ultrasound beam and a returning echo can be six orders of magnitude different.

#### History and etymology

The "decibel" is technically one tenth of the unit "bel," although the "bel" is rarely used. The bel is named in honor of Scottish-American scientist and inventor of the telephone, Alexander Graham Bell (1847-1927), which is why the 'B' is capitalized in 'dB' 2.