Example of Sound Level Averaging
Sound is measured using the logarithmic decibel (dB) scale. Therefore, by definition, a 10 db increase in sound is equal to a tenfold (101) increase in the mean square sound pressure of the reference sound. A 20 dB increase is a 100-fold (102) increase in the mean square sound pressure of the reference sound. A 30 dB increase is a 1,000-fold (103) increase in mean square sound pressure.
A logarithmic scale requires different mathematics than are used with linear scales. The sound pressures of two separate sounds, expressed in dB, are not averaged arithmetically. In the example shown below, two sound levels of equal duration are averaged. One has a level of 100 dB, the other 50 dB. Using conventional arithmetic, the average would be 75 dB. The true result, using logarithmic math, is 97 dB. This is because 100 dB has far more energy than 50 dB (100,000 times as much!) and is overwhelmingly dominant in computing the average of the two sounds.
