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A point source at origin is emitting sound waves. Intensity at a distance 1m from the origin is $16 \times 10^{- 8} {Wm}^{- 2}$ . The difference in intensity (magnitude only) at two points located at a distances of 2m and 4m from the origin respectively will be _______ $\times 10^{- 8} {Wm}^{- 2}$

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answer is 3.

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Detailed Solution

$We know for point source, I = \frac{P}{4 π r^{2}}$

At r = 1 m, $P = I \times 4 π r^{2} = 16 \times 10^{- 8} \times 4 π W$

At r = 2 m, $I_{1} = \frac{P}{4 π r^{2}} = \frac{16 \times 10^{- 8} \times 4 π}{4 π \times 4} = 4 \times 10^{- 8} W / m^{2}$

At r = 4 m, $I_{2} = \frac{P}{4 π r^{2}} = \frac{16 \times 10^{- 8} \times 4 π}{4 π \times 16} = 1 \times 10^{- 8} W / m^{2}$

Difference, $I_{1} - I_{2} = 3 \times 10^{- 8} W / m^{2}$

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