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 $8\, km$ away. Let the intensity of this faint sound be $30 \, dB$. The clock is situated $80\, m$ 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}=80\, m , $
$L _{2}=?$
$r _{1}=8000 \,m,$
$ L _{1}=30 \,dB$
$L =10 \log _{10}\left(\frac{ I }{ I _{0}}\right)$
Intensity due to a point source, $I \propto \frac{1}{ r ^{2}}$
$L _{2}- L _{1}=10 \log _{10}\left(\frac{ I _{2}}{ I _{0}}\right)-10 \log _{10}\left(\frac{ I _{1}}{ I _{0}}\right)$
$L _{2}- L _{1}=10 \log _{10}\left(\frac{ I _{2}}{ I _{1}}\right)=10 \log _{10}\left(\frac{ r _{1}^{2}}{ r _{2}^{2}}\right)$
$L _{2}-30=10 \log _{10}\left(10^{4}\right)=40$
$L _{2}=70 \,dB$