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# How to combine decibels for effective soundproofing

For effective soundproofing solutions one has to know** how to combine decibels. **First and foremost, sound from the loudest source will always dominate the overall sound level.

The human ear is capable of detecting changes in atmospheric pressure that is interpreted by our brains as sound. The ear cannot detect static (or steady state) pressure changes – they must be dynamic and oscillate between about 20 to 20,000 Hz. The minimum dynamic pressure change that the ear can detect is on the order of 20 micro-pascals (20 x 10^{-6 }N/m^{2}) or 0.2 billionth of atmospheric pressure! The maximum dynamic pressure change that the ear can detect is one million times the minimum pressure, or 120 dB. Because of the wide range of pressure variations that the ear can detect, the decibel scale is used, which describes the ratio of a dynamic pressure variation to a reference pressure, usually the minimum detectable pressure of 20 micro-pascals.

Are you good at math? How to combine decibels is a function of a math equation. Because sound pressure levels are described in a logarithmic scale, it is not possible to combine the noise from one source to the other by simply adding their decibel values. The sum is derived by the following equation:

where: SPL_{sum} is the sum of the noise levels

SPL_{i} are the sound pressure levels of the sources

So, in our example, the sum of two sources producing 80 dB each is 10*log_{10 }(10^{8 }+ 10^{8}) = 83 dB.

There are certain implications that should be recognized because sound adds in a logarithmic manner, and these implications are useful for soundproofing. Remember, *sound from the loudest source will always dominate the overall sound level*. For example, if one source of sound had a noise level of 70 dB and another source was at 80 dB, the combined sound level will be 80.4 dB. That is because 70 dB is a factor of 10 times less than 80 dB in the above equation. Therefore, for soundproofing purposes, it will always be more effective to address the loudest sources of noise first, since eliminating the quieter sources will not have an effect on the overall noise level. It also follows that if a noise source is 6 dB lower than the loudest noise sources, it can be ignored, since it will result in an increase of only 1 dB in the overall sound level.

One of the questions we are often asked is, “How many noise sources do we need to treat to obtain a noticeable difference in loudness?” This is easily answered by the above equation which explains how to combine decibels. Assuming that we have ten independent sound sources, each producing 100 dB, the combined sound pressure level will be 110 dB, as shown in Figure 1. If we are capable of attenuating each sound source by 20 dB (to 80 dB), the effects of treating the first nine sources are gradual, resulting in a 10 dB overall noise attenuation. However, when the final source is treated, we are able to obtain an additional 10 dB noise reduction to 90 dB overall. That is not to say that in all cases, it is necessary to treat all noise sources. It is, however, important to identify only the loudest noise sources and provide only as much noise attenuation needed to reduce their noise to be equal to that of other noise sources.

Sonic-Shield has an engineering staff with advanced technical capabilities who can assist individuals and companies in the testing, analysis and solution of noise problems including how to combine decibels. We can perform the required tests and analyses to arrive at a solution, as well as develop and supply the appropriate sound abatement materials and products to solve your noise problems. Knowing how to combine decibels is just one of the ways we can develop a solution for your noise problem.