Question

Match the following columns. Here, $I$ represent intensity, $A$ amplitude and $r$ distance from the source.
Column $\text{I}$ Column $\text{II}$
$a.$ $I$ due to point source $p.$ $\propto r^{-1/2}$
$b.$ $A$ due to point source $q.$ $\propto r^{-1}$
$c.$ $I$ due to line source $r.$ $\propto r^{-2}$
$d.$ $A$ due to line source $s.$ $\propto r^{-4}$

• A. $a-r,b-q,c-q,d-p$
• B. $a-p,b-q,c-r,d-s$
• C. $a-q,b-q,c-s,d-r$
• D. $a-r,b-p,c-q,d-r$

Answer 1

The correct option is A $a-r,b-q,c-q,d-p$

We know that intensity is given by,
$I=\frac{\text{P}}{\text{A}}$, where $P$ is power and $A$ is area.
For point source,
$A=4\pi r^2$
So, for same power,
$I\propto r^{-2}$ ..............(1)

For line source,
$A=2\pi rl$
[$l$ is length of source]
So, for same power,
$I\propto r^{-1}$ .............(2)
Also,
We know that, intensity
$I\propto A^2$
$\Rightarrow A\propto \sqrt{I}$
Hence, for point source,
$A\propto r^{-1}$ [from (1)]
and for line source,
$A\propto r^{-1/2}$ [from (2)]
Therefore, correct matching is
$a-r,b-q,c-q,d-p$