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About Decibels (dB)

Prepared by Gregg Vanderheiden Ph.D.
Trace R&D Center   University of Wisconsin-Madison

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

dB and Voltage gain    (20dB = 10x)

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

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.  

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

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

The following is from the Acoustics FAQ. 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.