First slide

Intensity of

Question

A person is standing at a distance D from an isotropic point source of sound. He walks 50.0 m towards the source and observes that the intensity of the sound has doubled. His initial distance D from the source is

Moderate

A

$50 \sqrt{2} m$
B

$\frac{50 \sqrt{2}}{\sqrt{2} - 1} m$
C

$\frac{50}{\sqrt{2} - 1} m$
D

$100 \sqrt{2} m$

Solution

Using $\frac{P}{4 {πR}^{2}} = I$
$\Rightarrow \frac{\frac{P}{4 π {(D - 50)}^{2}}}{\frac{P}{4 {πD}^{2}}} = \frac{2}{1} \Rightarrow \frac{D^{2}}{{(D - 50)}^{2}} = 2$
$\Rightarrow D = \sqrt{2} (D - 50) \Rightarrow (\sqrt{2} - 1) D = 50 \sqrt{2}$
$\Rightarrow D = \frac{50 \sqrt{2}}{\sqrt{2} - 1} = 170.7 m$

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