Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Decibels, Loudness, and Perception
Name: Robert S.
Status: other
Age: 50s
Location: N/A 
Country: N/A
Date: 9/15/2004


Question:
According to the answer to the Fifth Grade Class,

http://www.newton.dep.anl.gov/webpages/askasci/phy99/phy99405.htm

and I quote:

"decibel levels"

"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.


Replies:
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:

http://www2.sfu.ca/sonic-studio/handbook/index.html

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 sub-woofers.

Vince Calder


Dear Robert,

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 1000% increase.

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 industry standard.

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.

Bob Erck


Robert,

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.

Sincerely,

Bob Trach


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 powers 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 wave.

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.

good luck-

Jim Swenson



Click here to return to the Engineering Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (help@newton.dep.anl.gov), or at Argonne's Educational Programs

NEWTON AND ASK A SCIENTIST
Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory