At a distance of 5.0 m from a point source, the intensity of sound is 1.0 × 10^ -8 W m^ -2 . Determine the intensity at a distance of 25 m from the source.

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Quantrex Academy · Accepted Answer

Correct answer: D. 4.0 × 10^ -10 W m^ -2

For a point source, the intensity of sound

I

is inversely proportional to the square of the distance

r

from the source.

I \propto \dfrac{1}{r^2}

\Rightarrow \dfrac{I_2}{I_1} = \left(\dfrac{r_1}{r_2}\right)^2

Given

I_1 = 1.0 \times 10^{-8} \text{ W m}^{-2}

,

r_1 = 5.0 \text{ m}

, and

r_2 = 25 \text{ m}

.

\dfrac{I_2}{1.0 \times 10^{-8}} = \left(\dfrac{5.0}{25}\right)^2

\dfrac{I_2}{1.0 \times 10^{-8}} = \left(\dfrac{1}{5}\right)^2 = \dfrac{1}{25}

I_2 = \dfrac{1.0 \times 10^{-8}}{25} = 0.04 \times 10^{-8} \text{ W m}^{-2}

I_2 = 4.0 \times 10^{-10} \text{ W m}^{-2}

At a distance of 5.0 m from a point source, the intensity of sound...

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