Question

For a point source of sound, the graph of intensity $\left(I\right)$ versus square of distance from the source $\left(r^2\right)$ is best represented by

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Intensity is the energy per unit area per unit time.

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



For constant power $P$,

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

$\Rightarrow r^{2}I=$ constant $.....\left(1\right)$

Equation $\left(1\right)$ is similar to the equation of a hyperbola i.e.

$xy=$constant.

Hence, option $\left(d\right)$ is correct as it represents the graph of hyperbola.