A point source is emitting sound waves of intensity 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

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Solution

Q.
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 ____ $\times 10^{- 8}$ $W m^{- 2} .$ [2024]

Ans.
(3)

We know for point source, $I \propto \frac{1}{r^{2}} = \frac{K}{4 π r^{2}}$

$r_{1} = 2 m, r_{2} = 4 m = 2 r_{1}$

$I_{0} = 16 \times 10^{- 8} {W/m}^{2}$

at 2m, $I_{1} = \frac{I_{0}}{{(2)}^{2}} = \frac{16 \times 10^{- 8}}{4}$

$I_{1} = 4 \times 10^{- 8}$

At 4m, $I_{2} = \frac{I_{0}}{4^{2}} = \frac{16 \times 10^{- 8}}{16} = 10^{- 8}$

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

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