2-5 Intensity and sound level
The sound level - The decibel scale

The range of sound intensities the human ear can detect is quite large. For example, at a frequency of 1 kHz, the intensity of the lowest sound you can hear is about 10-12 W/m2 and the intensity of the highest sound you can tolerate without pain is about 1 W/m2.  Over this range, your perception of the sound loudness is not linear with the sound intensity. This allows your ear to be sensitive for very low sound intensities and at the same time be able to detect sounds which are 1012 times as large in intensities. You need to increase the sound intensity roughly by 10 times for your ear to feel that its loudness is doubled.  Because of the huge range of the sound intensities you can hear and the way you perceive loudness, it is more convenient to use a logarithmic scale of sound intensities to express sound levels. The sound level b is defined as