Question

The intensity of the waves from a point source at a distance d from the source is I. At what distance from the sources is the intensity equal to 2I

Answer 1

Answer:$d'=\frac{d}{\sqrt{2}}$

Explanation:

Intensity of the waves from a point source can be given by Power divided by surface area.

For P Power source and at a distance d from source Intensity is given by

$I=\frac{P}{\pi\cdot d^2}--------1$

when intensity is 2I then it is at a distance of let say d'

$2I=\frac{P}{\pi\cdot d'^2}--------2$

Divide 1 and 2 we get

$\frac{I}{2I}=\frac{P}{\pi\cdot d^2}\times \frac{\pi\cdot d'^2}{P}$

$\frac{1}{2}=(\frac{d'}{d})^2$

$\frac{d'}{d}=\frac{1}{\sqrt{2}}$

$d'=\frac{d}{\sqrt{2}}$