A (point source) source of sound emits waves osotropically in three dimensions. If the intensity at a distance $r_{0}$ from source is $I_{)} 0$ at what distance from the source is the intensity $0.100 I_{0}$ ?

1.16 r_{0}

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2.16 r_{0}

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3.16 r_{0}

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4.16 r_{0}

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Solution

The correct option is B $2.16 r_{0}$
Given an intensity of $I_{o}$ at a distance of $r_{o}$ from the point source

Let us suppose that the distance at which intensity becomes $0.100 \times I_{o}$ is $r_{d}$ .

We know that the intensity of a sound wave which is three dimensional is proportional to the
Inverse of the cube of the distance from the source i.e.
$I \propto \frac{1}{r^{3}}$

This means that
$I \times r^{3} = c o n s t a n t$

So,
$I_{o} \times r_{o}^{3} = (0.100 I_{o}) \times r_{d}^{3}$

$r_{d}^{3} = 10 \times r_{o}^{3}$

$r_{d} = 2.16 r_{o}$

So B is the correct answer.

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A (point source) source of sound emits waves osotropically in three dimensions. If the intensity at a distance r0 from source is I)0 at what distance from the source is the intensity 0.100 I0?

A (point source) source of sound emits waves osotropically in three dimensions. If the intensity at a distance $r_{0}$ from source is $I_{)} 0$ at what distance from the source is the intensity $0.100 I_{0}$ ?