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Relationship Between Watts and dBs

by August 30, 2004

Q: Can someone please explain the relationships between watts and dB's to me? I am new to audio and wish to acquire a better understanding of power/watts, etc. Thanks.

A: Decibel (dB)
(1) a logarithmic scale used to denote a change in the relative strength of an electric signal or acoustic wave. It is a standard unit for expressing the ratio between power and power level. Using the logarithmic relationship for power PdB = 10*log[Pout/Pin] , a doubling of electrical power only yields an increase of +3 dB. Increasing the power tenfold will yield an increase of +10 dB and is a doubling of perceived loudness. The decibel is not an absolute measurement, but indicates the relationship or ratio between two signal levels.

(2) SPL (sound pressure level) can be measured in dB. 0 dB represents the threshold of normal human hearing, 130 dB represents the threshold for pain, 140 dB causes irreparable hearing damage, and 150 dB can cause instant deafness, anything greater than about 192 dB can kill you.

Sound dB-SPL
Jet engine at 3m 140
Threshold of pain 130
Rock concert 120
Accelerating motorcycle at 5m 110
Pneumatic hammer at 2m 100
Noisy factory 90
Vacuum cleaner 80
Busy traffic 70
Quiet restaurant 50
Residential area at night 40
Empty movie house 30
Rustling of leaves 20
Human breathing (at 3m) 10
Threshold of hearing (good ears) 0

The relationship between sound amplitude and actual loudness is complex. Loudness is a perceptual dimension while sound amplitude is physical. Since loudness sensitivity is closer to logarithmic than linear in amplitude (especially at moderate to high loudnesses), we typically use decibels to represent sound amplitude, especially in spectral displays.

Weighting Networks

"A","B","C" and Linear are the standard weighting networks available. These are frequency filters that cover the frequency range of human hearing (20 Hz to 20 kHz)."A" weighting is the most commonly used filter in both industrial noise applications (OSHA) and community noise regulations. "A" weighted measurements are often reported as dBA. The "A" weighted filter attempts to make the dosimeter respond closer to the way the human ear hears. It attenuates reduces the frequencies below several hundred hertz as well as the high frequencies above six thousand hertz. "B" weighting is similar to "A" weighting but with less attenuation. The "B" weighting is very seldom, if ever, used. "C" weighting provides a fairly flat frequency response with only slight attenuation of the very high and very low frequencies. "C" weighting is intended to represent how the ear perceives sound at high decibel levels and is often used as a "flat" response when Linear is not available. "C" weighted measurements are often reported as dBC. Linear is thought of as having a flat frequency response curve over the entire measurement frequency range. Linear is most commonly found on upper model sound level meters and is typically used when performing octave band filter analysis.

Watt - a unit of electrical power. A watt of electrical power is the use of one joule of energy per second. Watts of electrical power equals volts times amperes.

Watts dB (rel to 1 watt)
1 0
2 3.01029996
5 6.9897
10 10
50 16.9897
100 20
200 23.0103
300 24.7712125
400 26.0205999
500 26.9897
600 27.7815125
700 28.4509804
800 29.0308999
900 29.5424251
1000 30

Power: (in this discussion), refers to watts. Power defined is the rate at which energy is converted or dissipated, as in the case of an amplifier driving a loudspeaker. It is important in our discussion in defining the general relationship.

A simple chart will help to understand the relationship of the terms we have introduced:

dB Change Voltage multiplier Power multiplier Loudness multiplier
3 1.4 2 1.23
6 2 4 1.52
10 3.16 10 2
20 10 100 4
40 100 1000 16

Enjoy the music, but practice safe listening...

Here is a link for  Safe Listening Levels which gives soem basic guidelines form OSHA.

For a quick swag estimate on how much power you may need to reach desired SPL levels in your home theater system, try this calculator.

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About the author:

Gene manages this organization, establishes relations with manufacturers and keeps Audioholics a well oiled machine. His goal is to educate about home theater and develop more standards in the industry to eliminate consumer confusion clouded by industry snake oil.

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