Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Intensity is 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 ...........(1)
Equation (1) is similar to the equation of hyperbola $xy=$constant.
Hence, option $\left(d\right)$ is correct which represents the graph of hyperbola.