Question

The reference pressure amplitude $\Delta P_{M_0}$ is often taken to be $3.0\times {10}^{-5}N/m^2$ corresponding to an intensity of $1.0\times {10}^{-12}W/m^2$. What would the sound level be if $\Delta P_M$ were $1atm$?

Answer 1

As we know,

$\beta \left(dB\right)=20log\frac{\Delta P_M}{\Delta P_{M_0}}$

then ,

$\beta \left(dB\right)=20log\frac{1\times {10}^5}{3.0\times {10}^{-5}}$

$\beta \left(dB\right)=20log\frac{1}{3}+20log\left({10}^{10}\right)$

$\beta \left(dB\right)=20\times (-0.4771)+20\times 10$

$\beta \left(dB\right)=190.46$ decibels.