Question

If the intensity is increased by a factor $x$, sound level is increased by $20\text{dB}$. Then, the value of $x$ is

Answer 1

We know that, Loudness ($\beta$) is related to intensity of sound ($I$) as,
$\Delta \beta =10{\log }_{10}\left(\frac{I}{I_0}\right)$
From the data given in the question,

$20=10{\log }_{10}\left(\frac{I}{I_0}\right)[\because \Delta \beta =20\text{dB}]$

$\Rightarrow \frac{I}{I_0}={10}^2=100$

$\Rightarrow I=100I_0$

Comparing with $I=x{I}_0$ we get, $x=100$