Question

If the intensity of a wave at a distance $r$ from a point source is $A,$ the intensity at distance $2r$ will be-

• A. $2A$
• B. $A$
• C. $\frac{A}{2}$
• D. $\frac{A}{4}$

Answer 1

The correct option is D $\frac{A}{4}$

Intensity is given by,

$I=\frac{\text{power}}{\text{area}}$

$I=\frac{P}{4\pi r^2}$

$\Rightarrow I\propto \frac{1}{r^2}$

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

Here, $r_1=r;r_2=2r;I_1=A$

$\Rightarrow \frac{I_1}{I_2}={\left(\frac{2r}{r}\right)}^2$

$\Rightarrow I_2=\frac{A}{4}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.