Question

The clocktower ("ghantaghar") of Dehradun is famous for the sound of its bell, which can be heard, albeit faintly, upto the outskirts of the city $8km$ away. Let the intensity of this faint sound be $30dB$. The clock is situated $80m$ high. The intensity at the base of the tower is :-

• A. 60 dB.
• B. 70 dB.
• C. 80 dB.
• D. 90 dB.

Answer 1

Answer: (B)

$r_2=80m,$
$L_2=?$
$r_1=8000m,$
$L_1=30dB$
$L=10{\log }_{10}\left(\frac{I}{I_0}\right)$
Intensity due to a point source, $I\propto \frac{1}{r^2}$
$L_2-L_1=10{\log }_{10}\left(\frac{I_2}{I_0}\right)-10{\log }_{10}\left(\frac{I_1}{I_0}\right)$
$L_2-L_1=10{\log }_{10}\left(\frac{I_2}{I_1}\right)=10{\log }_{10}\left(\frac{r_1^2}{r_2^2}\right)$
$L_2-30=10{\log }_{10}\left(10^4\right)=40$
$L_2=70dB$