Question

A point source is emitting sound in all directions. The ratio of distance of two points from the point source where the difference in loudness levels is $3 \,dB$ is: $\left(\log _{10} 2\right.$ $=0.3$ )

• A. $\frac{1}{2}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\frac{1}{4}$
• D. $\frac{2}{3}$

Answer 1

Answer: (B)

$dB =10 \log \left(\frac{I}{I_{0}}\right)$
$=10 \log \left(\frac{K / r^{2}}{I_{0}}\right)$
$=10\left[\log \left(K'\right)-2 \log r\right]$
$d B_{1}=10\left(\log K'-2 \log r_{1}\right)$
$d B_{2}=10\left(\log K'-2 \log r_{2}\right)$
$3=d B_{1}-d B_{2}=20 \log \left(\frac{r_{2}}{r_{1}}\right)$
$(0.3)=\log \left(\frac{r_{2}}{r_{1}}\right)^{2}$
$\Rightarrow \left(\frac{r_{1}}{r_{2}}\right)=\frac{1}{\sqrt{2}}$