Earlier, we discussed the relationship between sound pressure, sound energy, and decibels. To complete the discussion, we also need to include the human perception of changes in sound. The left column shows a factor increase in relative sound energy, the middle column shows the corresponding increase in decibels, and the right column shows the human perception of these changes.
The same relationships hold true for noise decreases. For instance, a change of 0.5 times the relative energy corresponds with a decrease of 3 dBA, which is also barely perceptible; 0.316 times the relative energy reduces the noise level by 5 dBA, which is readily perceptible, and so on.
The first two columns exhibit an objective, mathematical relationship, but the third column is based on studies involving thousands of human volunteers over many years. These studies included laboratory tests in which a standard recorded noise was played at a reference level and various other levels. Test subjects gave their subjective reactions after each comparison of the level of interest and the reference level.