If the threshold of hearing is assumed to be the reference $(0\ dB)$ , then the threshold of pain is taken to be $120\ dB$ . Let the corresponding sound intensities be $I_0$ and $I$ respectively. Then $\frac{{{I_0}}}{I}$ is
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$0=10 \log \left(\frac{\mathrm{I}_{0}}{10^{-12}}\right) \Rightarrow \mathrm{I}_{0}=10^{-12}$
$120^{\circ}=10 \log \left(\frac{\mathrm{I}}{10^{-12}}\right)$
$\Rightarrow \frac{\mathrm{T}}{10^{-12}}=10^{12} \Rightarrow \mathrm{I}=1 \Rightarrow \frac{\mathrm{I}_{0}}{\mathrm{I}}=10^{-12}$
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