# Decibel

Last revised by Andrew Murphy on 31 Mar 2020

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, we use decibel as a unit of "loudness," but what exactly is "loudness"? "Loudness" is an informal way of expressing a sound's intensity, 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

So, 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 Socttish-American scientist and inventor of the telephone, Alexander Graham Bell (1847--1927) 2.