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A point source is emitting sound waves of intensity $$16 \times 10^{-8}$$ W m$$^{-2}$$ at the origin. The difference in intensity (magnitude only) at two points located at distances of 2 m and 4 m from the origin respectively will be ________ $$\times 10^{-8}$$ W m$$^{-2}$$.
Correct Answer: 3
For a point source,
$$I\propto\frac{1}{r^2}$$
Given intensity at source reference (at 1 m, implied) is
$$I_0=16\times10^{-8}\ \text{W/m}^2$$
At r=2m,
$$I_1=\frac{16\times10^{-8}}{2^2}$$
$$=4\times10^{-8}$$
At r=4m,
$$I_2=\frac{16\times10^{-8}}{4^2}$$
$$=1\times10^{-8}$$
Difference in intensity:
$$\left|I_1-I_2\right|$$
$$=(4-1)\times10^{-8}$$
$$=3\times10^{-8}$$
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