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 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) |
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?
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-à-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 listed.