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About Decibels

From: Gregg Vanderheiden <gv@trace.wisc.edu>
Date: Sat, 30 Oct 2004 23:16:05 -0500
To: <w3c-wai-gl@w3.org>
Message-ID: <auto-000147922819@spamarrest.com>

About Decibels (dB)

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

dB and Power   (20dB = 100x)

When talking about power, a 3dB represents a ration 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)


Sound Environment

Sound Pressure Level (dBA SPL)

Approximate loudness with regard to ordinary conversation

Threshold of hearing


Don’t hear anything

Broadcast studio interior or rustling leaves


1/32nd as loud as conversation

Quiet house interior or rural nighttime


1/16th as loud

Quiet office interior or watch ticking


1/8th as loud

Quiet rural area or small theater 


1/4th as loud

Quiet suburban area or dishwasher in next room


1/2 as loud

Office interior or ordinary conversation


Ordinary Conversation

Vacuum cleaner at 10 ft.


Twice as loud

Passing car at 10 ft. or garbage disposal at 3 ft


4 times as loud

Passing bus or truck at 10 ft. or food blender at 3 ft.


8 times as loud

Passing subway train at 10 ft. or gas  lawn mower at 3 ft.


16 times as loud

Night club with band playing


32 times as loud

Threshold of pain 


64 times as loud as conversation
(twice as loud as night club)

Where to get more information.

 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 


What is difference between dB SPL  and dB(A) SPL? 

 The following is from http://www.campanellaacoustics.com/faq.htm

A sound level meter that measures the sound pressure level with a "flat"
response will indicate the strength of low frequency sound with the same
emphasis as higher frequency sounds. Yet our ear perceives low frequency
sound to be of less loudness that higher frequency sound. The eardrum-
stapes-circular window system behaves like a mechanical transformer with a
finite pass band. In EE parlance, the "3 dB" rollover frequencies are
approximately 500 Hz on the low end and 8 kHz on the high end. By using an
electronic filter of attenuation equal to that apparently offered by the
human ear for sound each frequency (the 40-phon response curve), the sound
level meter will now report a numerical value proportional to the human
perception of the strength of that sound independent of frequency. Section
8.2 shows a table of these weightings. 

Unfortunately, human perception of loudness vis--vis frequency changes with
loudness. When sound is very loud - 100 dB or more, the perception of
loudness is more consistent across the audible frequency band. "B" and "C"
Weightings reflect this trend. "B" Weighting is now little-used, but
C-Weighting has achieved prominence in evaluating annoying community noises
such as low frequency sound emitted by artillery fire and outdoor rock
concerts. C-Weighting is also tabulated in 8.2. 

The first electrical sound meter was reported by George W Pierce in
Proceedings of the American Academy of Arts and Sciences, v 43 (1907-8) A
couple of decades later the switch from horse-drawn vehicles to automobiles
in cities led to large changes in the background noise climate. The advent
of "talkies" - film sound - was a big stimulus to sound meter patents of the
time, but there was still no standard method of sound measurement. "Noise"
(unwanted sound) became a public issue. 

The first tentative standard for sound level meters (Z24.3) was published by
the American Standards Association in 1936, sponsored by the Acoustical
Society of America. The tentative standard shows two frequency weighting
curves "A" and "B" which were modeled on the response of the human ear to
low and high levels of sound respectively. 

With the coming of the Walsh-Healy act in 1969, the A-Weighting of sound was
defacto presumed to be the "appropriate" weighting to represent sound level
as a single number (rather than as a spectrum). With the advent of US FAA
and US EPA interests in the '70's, the dBA metric was also adapted by them.
(Along with the dBA metric has come an associated shortfall in precision in
accurately representing the capacity of a given sound to produce hearing
loss and the capacity to create annoyance.) 

[Editor's Note: A single number metric such as dBA is more easily understood
by legal and administrative officials, so that promulgation, enforcement and
administrative criteria and actions are understandable by more parties,
often at the expense of a more precise comprehension and engineering action
capability. For instance, enforcement may be on a dBA basis, but noise
control design demands the octave-band or even third-octave band spectral
data metric.] 

The most commonly referenced weighting is "A-Weighting" dB(A), which is
similar to that originally defined as Curve "A" in the 1936 standard.
"C-Weighting" dB(C), which is used occasionally, has a relatively flat
response. ""U-Weighting"" is a recent weighting which is used for measuring
audible sound in the presence of ultrasound, and can be combined with
A-Weighting to give AU-Weighting. The A-Weighting formula is given in
section 8 of this FAQ file. 

In addition to frequency weighting, sound pressure level measurement can be
time-weighted as the "Fast", "Slow" or "Impulse" response. Measurements of
sound pressure level with A-Weighting and fast response are also known as
the "sound level". 

Many modern sound level meters can measure the average sound energy over a
given time. this metric is called the "equivalent continuous sound level" (L
sub eq). More recently, it has become customary in some circles to presume
that this sound measurement was A-Weighted if no weighting descriptor is




Gregg C Vanderheiden Ph.D. 
Professor - Depts of Ind. Engr. & BioMed Engr.
Director - Trace R & D Center 
University of Wisconsin-Madison 
< <http://trace.wisc.edu/> http://trace.wisc.edu/> FAX 608/262-8848  
For a list of our list discussions http://trace.wisc.edu/lists/



Received on Sunday, 31 October 2004 04:16:31 UTC

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