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Question
The intensity of sound from a point source is 1.0 × 10−8 W m−2 at a distance of 5.0 m from the source. What will be the intensity at a distance of 25 m from the source?
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Solution
Given:
The intensity I1 is 1.0 × 10−8 Wm−2,
when the distance of the point source \[r_1\]is 5 m.
Let I2 be the intensity of the point source at a distance \[r_2\]= 25 m.
As we know,
\[I \propto \left( \frac{1}{r^2} \right) . \]
\[\text { So }, \]
\[\frac{I_1}{I_2} = \frac{{r_2}^2}{{r_1}^1}\]
\[ \Rightarrow I_2 = \frac{I_1 {r_1}^2}{{r_2}^2}\]
On substituting the respective values, we get:
\[ I_2 = \frac{1 . 0 \times {10}^{- 8} \times 25}{625}\] \[ = 4 . 0 \times {10}^{- 10} \text { W/ m }^2\]
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