20230114153200 Decibels in audio

Sound pressure and decibels in audio

Sound pressure is the change in local atmospheric pressure caused by sound waves. This value is measured in Pascals (1 Pascal = 1 Pa = 1 Newton per square meter). Humans can hear sound at roughly 0.000002 Pa = $2\times 10^{-5}$ Pa = 20 μPa. (This is equivalent to the sound of a mosquito flying 3 meters away.) Sound at 20 Pa is when it starts to become physically painful to hear.

In short, the range of a human’s hearing is $2\times 10^{-5}$ Pa to 20 Pa.

For the sake of convenience, we define 0 dB SPL = $10^{-5}$ Pa. dB SPL is logarithmic:

Pa	dB SPL
0.00002	0
0.0002	20
0.002	40
0.02	60
0.2	80
2	100
20	120

To calculate dB SPL from sound pressure: $L_p=20{\log }_{10}\frac{p}{p_0}\text{dB}$

where $p_0=20\text{μPa}$.