Prepared by Gregg Vanderheiden Ph.D.

Trace R&D Center   Univ of Wisc.

## What is a Decibel (dB)?

A dB or Decibel is a logarithmic unit of measure of the ratio between two numbers.

## dB and Power   (20dB = 100x)

When talking about power, a 3dB represents a ratio of two to one or a doubling of power.

·         Thus,  a gain of 10dB would represent a ratio of ten to one for power - so 10 dB be 10 times the power

·         A 40dB power gain would be 10,000 times the power.

## dB and Voltage gain    (20dB = 10x)

When talking about voltage, 6dB represents a ratio of two to one or a doubling of voltage.

·         20dB would represent a ratio of ten to one for voltage - so 20 dB would be 10 times the voltage.

·         A 40dB voltage gain would be 100 times the voltage.

## dB SPL (Sound Pressure Level)  (20dB = 10x)

The term “SPL” stands for sound pressure level. SPL measures are taken with respect to the minimum threshold for human hearing.  A 20 dB difference in SPL represents a ratio of ten-to-one in sound pressure.

·         Thus, a  40dB SPL would be a sound pressure level that is 100 times greater than the sound pressure level of the quietest sound that normal human hearing can detect.

## Perception of Loudness   (20dB = 4x)

Interestingly, our perception of loudness is not the same as sound pressure level.   Although the actual formulae

is somewhat complex,  as a rough rule of thumb, an increase of 10db SPL is perceived to be approximately twice as loud.

·         Thus a 20 Db gain would seem to be about 4 times as loud.

·         And a 40 Db gain would seem to be about 16 times as loud.

## dB SPL in Real Life

To give you an idea of how a dB SPL measurements relate to daily life, a listing of the approximate sound pressure level for various sounds is provided below.  (From http://www.state.me.us/spo/landuse/docs/NoiseTABulletin.pdf - with the “Approximate Loudness” column added)   (see also  dB SPL and dB(A) SPL discussion on next page)

 Threshold of hearing 0 dBA SPL Don’t hear anything Broadcast studio interior or rustling leaves 10 dBA SPL 1/32nd as loud as conversation Quiet house interior or rural nighttime 20 dBA SPL 1/16th as loud Quiet office interior or watch ticking 30 dBA SPL 1/8th as loud Quiet rural area or small theater 40 dBA SPL 1/4th as loud Quiet suburban area or dishwasher in next room 50 dBA SPL 1/2 as loud Office interior or ordinary conversation 60 dBA SPL Ordinary Conversation Vacuum cleaner at 10 ft. 70 dBA SPL Twice as loud Passing car at 10 ft. or garbage disposal at 3 ft 80 dBA SPL 4 times as loud Passing bus or truck at 10 ft. or food blender at 3 ft. 90 dBA SPL 8 times as loud Passing subway train at 10 ft. or gas lawn mower at 3 ft. 100 dBA SPL 16 times as loud Night club with band playing 110 dBA SPL 32 times as loud Threshold of pain 120 dBA SPL 64 times as loud as conversation (twice as loud as night club)

A good resource on this topic (referred to from the Acoustical Society of America Site  http://asa.aip.org/)

·         Acoustics FAQ  -  http://www.campanellaacoustics.com/faq.htm