Waves

JEE Main level, numerical answer, medium

30 of 142

Question 30 of 142

A point source is emitting sound waves of intensity 16×10−8Wm−216\times {10}^{-8}W{m}^{-2} at the origin. The difference in intensity (magnitude only) at two points located at a distances of 2m2m and 4m4m from the origin respectively will be ________×10−8Wm−2\times {10}^{-8}W{m}^{-2}.

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Answer: 3

Intensity for a point source varies as I∝1r2I\propto \dfrac{1}{{r}^{2}}.
Intensity at a distance of 2m2m, I2=16×10−8×122=4×10−8Wm−2{I}_{2}=16\times {10}^{-8}\times \dfrac{1}{{2}^{2}}=4\times {10}^{-8}W{m}^{-2}
Similarly, intensity at a distance of 4m4m, I4=16×10−8×142=1×10−8Wm−2{I}_{4}=16\times {10}^{-8}\times \dfrac{1}{{4}^{2}}=1\times {10}^{-8}W{m}^{-2}
Required difference, I2−I4=3×10−8Wm−2{I}_{2}-{I}_{4}=3\times {10}^{-8}W{m}^{-2}

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