There’s more to decibels than meets the ear.

 I thought I knew what decibels (dB) were. One dictionary definition is “A decibel is a unit of measurement which is used to indicate how loud a sound is.” Some typical decibel values are

•  A normal conversation at a distance of 1m: 40-60 dB

• Possible hearing damage: 120 dB

• Jet engine 100m distant: 110-140 dB

Public Domain Image from publicdomainq.net

But decibels are much more complex. Because sound is caused by pressure on our ears, I assumed that the units for decibels would be pressure. They’re not; they’re pure numbers. Also not obvious is that the decibel scale is logarithmic. A ten decibel increase in dB units is an increase of ten times in sound intensity. A vacuum cleaner at 80 dB is 1,000 times noisier than a floor fan at 50dB. The logarithmic scale is useful for describing sound volume because our ears perceive an astonishing range of pressures:  an indoor rock concert is three million times as loud as the quietest audible sound.

Image by Georgiana Ionescu in the Electronics Collection

Image public domain from CoolCLIPS

But decibels are used for more than sound. They can actually be used to measure the ratio of the value of anything relative to a “standard” value. For sound, the standard reference value is a pressure of 20 micro-Pascals, which is the softest audible sound. Decibels are used most commonly to measure the amplitude or the power of sound and electricity.

Not so surprisingly, the decibel is one tenth of a bel. And the bel was created in the 1920’s to quantify the signal loss in telegraph and telephone circuits. It was created by Bell Telephone Laboratories and was named in honour of Alexander Graham Bell, inventor of the first practical telephone.

So finally: the formula for decibels is

Where Power 2 is the power being measured and Power 1 is the reference power.