KVPY 2020-21 SB SX Exam Previous Papers

Question : 28 of 120

Marks: +1, -0

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 :-

60 dB.
70 dB.
80 dB.
90 dB.

Validate

Solution:

{r}_{2}=80 {m}, \;\;{L}_{2}=?

{r}_{1}=8000 {m}, {L}_{1}=30 {dB}

{L}=10 \log _{10}({{I}}/{{I}_{0}})

Intensity due to a point source,

{I} \∝{1}/{{r}^{2}}

{L}_{2}-{L}_{1}=10 \log _{10}({{I}_{2}}/{{I}_{0}})-10 \log _{10}({{I}_{1}}/{{I}_{0}})

{L}_{2}-{L}_{1}=10 \log _{10}({{I}_{2}}/{{I}_{1}})=10 \log _{10}({{r}_{1}^{2}}/{{r}_{2}^{2}})

{L}_{2}-30=10 \log _{10}(10^{4})=40

{L}_{2}=70 {dB}

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