Decibels, Loudness, and Perception
Name: Robert S.
According to the answer to the Fifth Grade Class,
and I quote:
"Question: We are a 5th grade class and we would like information about
decibel levels. Do you have a list of decibel levels for common sounds?
Such as voice, airplane, etc?
Answer: First, remember that the decibel (dB) is a logarithmic unit,
meaning that you cannot add and subtract dB like ordinary numbers. For
example, an increase of 3 dB is a doubling of the "strength" of the sound,
and an increase of 10 dB means that the
sound is 10 times as loud; i.e., 70 dB is 10 times as loud as 60 dB."
The book that came with my BIC Venturi speakers states that an increase of
10 decibels in sound represents a DOUBLING of
the volume. That means that 70 dB would be TWICE as loud as 60 dB.
To quote the book:
"Psycho-acousticians agree that a change of 10 dB of sound pressure level
causes one to hear a DOUBLING of loudness."
Please help reconcile these two different sources.
At the risk of giving you more information about dB than you care to know,
I will direct you to the very comprehensive web site:
The term decibel (dB) is defined as dB = 10*log(P1/P0) where "log" is
base 10 and P1 and P0 are the actual sound excess pressure between two
pressures P1 and P0. If on that home page you click on the term decibel:
http://www2.sfu.ca/sonic-studio/handbook/Decibel.html you will see a
detailed explanation including typical dB levels for various sound/noise
sources. By convention 0 dB is the threshold of human hearing. This is
obviously pretty arbitrary because different people have different hearing
sensitivities. This introduces the distinction between sound "intensity" (a
physical measurement) and "loudness" (a sensory response). The analogy to
light is "wavelength" and "color" or more accurately "light intensity" and
"brightness". In both cases the former terms refer to a physical measurement
and the latter terms refer to a visual response. The need for a
logarithmetric scale in the case of sound and light is the very wide range
of human hearing and sight to an enormous range of sensory input. The
confusion arises when one attempts to relate the physical measurement of
sound intensity as measured in decibels and the perceived increase in the
physiological response termed "loudness". There are even different "scales"
that attempt to include a correction for the fact that human hearing can
respond (typically) from about 20 hertz (cycles/sec) to roughly 10
kilohertz. But the "cutoffs" are very different for various individuals and
changes with age, surroundings, etc. Because "loudness" is a psycho-physical
response, it can be said that an increase 10dB is a doubling in "loudness"
even though the dB scale is base 10 logarithmetric. It is really only a
rough comparison and an "apples and oranges" one at that. What to you might
seem like a huge increase in loudness in let us say music, may have a lot to
do with your particular "taste" in music. The current fad among the younger
set is sub-sonic booming that can rattle a car. To me that is very "loud"
even if the sound "intensity" may be very marginally different between two
The confusion here arises from the difference between the intensity of sound
(measured in watts/m^2) and the loudness of the sound as estimated by a
human listening to the sound. The perceived loudness is NOT proportional to
the intensity of the sound. It is more nearly proportional to the logarithm
of the intensity. This is what makes decibels such a useful measure.
It also illustrates the cleverness of evolution and explains why we can
clearly hear the quietest whispers and the buzz of a mosquito and still
understand and survive the sounds made by subways, jackhammers, and even
rock concerts with our hearing almost intact.
An increase in the sound intensity by a factor of 10 does increase the
decibel rating by adding 10. However, it is perceived by the ear as less.
For example, an increase of the decibel rating from 100 to 110 would be
perceived as roughly a 10% increase and NOT a factor of 10, which would be a
Technical details: Decibels are defined as B = 10 log (I/H) where I is the
sound intensity (usually measured in watts/m^2) and H is a reference
intensity, generally taken to be 1.0 E-12 W/m^2, which is about the
threshold of hearing for a normal ear in good health. To gain a feeling for
this equation, I find it very useful to do a few simple calculations with a
calculator which has a log function (base 10) and can take powers with base
10 (log (x) and 10^x). Note that these are inverse functions:
log(10^x) = 10^(log(x)) = x. 100 db gives I = 10^10*H while
110 db gives I = 10^11*H.
Some decibel ratings:
0 db Threshold of hearing
30 db Whisper
40 db Buzz of mosquito
50 db Normal conversation
70 db Vacuum cleaner
100 db Subway or power mower
120 db Rock concert
130 db Jackhammer or machine gun
150 db Nearby jet plane
Best, Dick Plano...
Here is the story about bels. (One tenth of a bel is a deci-bel!)
Intensity is the power density of a sound wave. It is proportional to the
square of the pressure.
The decibel scale is simply a way of comparing two sound intensity levels.
dB = 10 log(I/Io) where I is the intensity you are measuring, and Io is an
arbitrary reference number that that is 10^-16 watts per square centimeter.
Thus, if the noise has power of 10^-9 watts per square centimeter, the dB
level is 70. You can find decibel levels of common noises on the Internet.
Traffic is 70 dB, a whisper, 20 dB, etc.
Zero dB would be 10^-16 watts per square centimeter and this is very quiet.
If the sound is even quieter, the dB levels become negative.
Loudness, as perceived by a person, is fairly arbitrary. Also, it depends
on the frequency. If psycho-acousticians think that 10 dB sounds twice as
loud, then I will not dispute it.
There is another loudness scale that weights the number according to a how
well humans hear the frequency. This is the dBA scale. People in loud
factories make dBA sound measurements.
That is actual SOUND. The audio industry also uses the decibel as a way of
measuring signal levels. Not just signal levels, but ratios of signal
levels, both POWER and VOLTAGE.
First, dB can be used to measure an actual voltage or power: for example,
you will sometimes see "dBm." dBm = 10 log(P/Po) where Po is 1 milliwatt
of power across a 600 ohm load. This 600 ohm load comes from old telephone
For voltage, dB = 20 log(V/Vo). Yes, it is 20 instead of 10. For dBV, the
Vo value is 1 volt. There are other voltage scales too.
Second, dB can also be used as a way of measuring CHANGE. A preamplifier
might be rated as 40 dB gain which means it amplifies the voltage by one
hundred. That is, dB = 20 log(V/Vo) where V is the amplified voltage, and
Vo is the original voltage.
Sometimes audio equipment has a VU meter. This means "volume unit" meter.
Usually, 0 dB is the maximum signal level that the equipment can normally
operate at. Recording levels should be less than that, that is, negative.
The following is a list of DECIBEL INTENSITIES taken from Encarta 2005.
0 - Threshold of hearing
10 - rustle of leaves, a quiet whisper
20 - average whisper
20-50 - quiet conversation
40-45 - hotel, theater between performances
50-65 - loud conversation
65-70 - traffic on a busy street
65-90 - train
75-80 - factory noise( light/medium work)
90 - heavy traffic
90-100 - thunder
110-140 - jet aircraft at takeoff
130 - threshold of pain
140-190 - space rocket on takeoff
I hope that this helps.
I think your second source is the more nearly correct one, Robert,
because the key word you used in your question is "loudness".
The first source is also correct, but not about loudness, rather about
"power" in the sound wave,
in physical units of watts or watts/cm2 or similar.
This implies that the human body perceives ten times the sound-power as
being only twice as loud.
And 100 times the sound power is only 4 times as loud to our ears.
Weird but true.
And actually good for us, probably designed to that effect by evolution,
so that we can hear and effectively use the extremely wide range of sound
that frequently exist in various times and places.
Radios need to "hear" a similarly wide range of radio-wave power
densities, more than 100dB.
Most radios try to pretend there is no loudness difference at all.
But they can afford to be like that, because they never try to hear more
than one signal at a time.
Sound-power is not the electrical watts applied to your stereo speaker.
It's the sum of:
- the kinetic energy of the moving-air parts of the sound wave, and
- the potential energy of the pressure-peaks and -valleys in the sound
It goes as the square of the peak-to-valley pressure-change in the sound wave.
Is sound power proportional to electrical power applied to a speaker?
Hard to imagine that music (as reproduced from electronic signals) could
sound right if this wasn't true.
But the sound power is usually a tiny percentage of electrical power
applied, so maybe there are other possibilities.
Manufacturers rate their speaker efficiencies only as
a single decibel-number at a single electrical wattage number.
Maybe they have not figured it out either.
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Update: June 2012