Sound pressure Level

Intensity is proportional to pressure squared:

$$I \approx p^2/400$$

$$\approx p^2/\left(2^2 \times 10^2\right).$$

The sound pressure level $L_p$ (SPL) is equivalent to sound intensity level and is expressed in dB by:

$$L_p = \textcolor{blue}{10\log I/I_0}$$

$$= \textcolor{blue}{10\log \left(p^2/\left(2^2 \times 10^2 \times 10^{-12} \right) \right) }$$

$$= \textcolor{blue}{10\log \left(p/(2\times 10^{-5})\right)^2}$$

$$= \textcolor{blue}{20\log p/(2\times 10^{-5})}$$

$$= \textcolor{blue}{20\log p/p_0}.$$

where $p_0 = 2\times 10^{-5}$ is the threshold of hearing for amplitude of pressure variations.