Question

At a distance of $10\text{m}$ from a point source, loudness is found to be $20\text{dB}$. The distance from the source where loudness is $0\text{dB}$ is

• A. $20\text{m}$
• B. $50\text{m}$
• C. $100\text{m}$
• D. $\infty$

Answer 1

The correct option is C $100\text{m}$

From the question we have
$10\text{log}\frac{I_1}{I_0}=20\Rightarrow I_1=100I_0$
Now for $0\text{dB},I_2=I_0$ as $I\propto r^2$
$\Rightarrow \frac{I_1}{I_2}={\left(\frac{r_2}{r_1}\right)}^2\Rightarrow r_2=r_1\sqrt{\frac{I_1}{I_2}}=10\sqrt{\frac{100I_0}{I_0}}$
$=100\text{m}$