Question 25

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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