Sound pressure Level (SPL or $L_p$)

Recall: intensity is proportional to pressure squared:

$$I = p^2/(\rho c),$$

(where $\rho c \approx 400$).

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

$$L_p = 10\log I/I_0$$

$$=$$

The product of $\rho$ and $c$ is often approximated by 400:

$$=$$

$$=$$

$$=$$

$$= .$$

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