Wave Mechanics Question 1094
Question: The intensity of sound from a radio at a distance of 2 metres from its speaker is $ 1\times {{0}^{-2}}\mu \ W/m^{2}. $ The intensity at a distance of 10 meters would be
[CPMT 2005]
Options:
A) $ 0.2\times {{10}^{-2}}\mu \ W/m^{2} $
B) $ 1\times {{10}^{-2}}\mu \ W/m^{2} $
C) $ 4\times {{10}^{-4}}\mu \ W/m^{2} $
D) $ 5\times {{10}^{-2}}\mu \ W/m^{2} $
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Answer:
Correct Answer: C
Solution:
$ I\propto \frac{1}{r^{2}}\Rightarrow \frac{I _{2}}{I _{1}}=\frac{r _{1}^{2}}{r _{2}^{2}} $
Therefore $ \frac{I _{2}}{1\times {{10}^{-2}}}=\frac{2^{2}}{10^{2}}=\frac{4}{100} $
Therefore $ I _{2}=\frac{4\times {{10}^{-2}}}{100} $ = $ 4\times {{10}^{-4}}\ \mu \ W/m^{2} $
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