Question

What is the maximum possible sound level in dB of sound waves in air ? Given that density of air is $1.3\times {10}^{5}N/m^2,\nu =332m/s$ and the atmospheric pressure $P=1.01\times {10}^{5}N/m^2$ .

Answer 1

For maximum possible sound intensity , maximum pressure amplitude of wave can be at most equal to atmospheric pressure . So , we have ,
$\Delta p_0=p=1.01\times {10}^{5}N/m^2$
$I=\frac{\Delta p{}_0^2}{2\rho v}=\frac{(1.01\times {10}^5{)}^2}{2\times 1.3\times 332}=1.18\times {10}^7\frac{W}{m^2}$

Thus loudness level is

$L=10log\left(\frac{I}{I_0}\right)=lo{g}_{10}\left(\frac{{10}^7}{{10}^{-12}}\right)=190dB$