Question

As a wave propagates,

• A. The wave intensity remains constant for a plane wave.
• B. The wave intensity decreases as the inverse of the distance from a line source.
• C. The wave intensity decreases as the inverse square of the distance from a point source.
• D. Total intensity of the spherical wave over the spherical surface centered at the source remains constant at all times

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A The wave intensity remains constant for a plane wave.
B The wave intensity decreases as the inverse of the distance from a line source.
C The wave intensity decreases as the inverse square of the distance from a point source.
D Total intensity of the spherical wave over the spherical surface centered at the source remains constant at all times

When the travelling wave is coming from a very far-off source, the wavefronts are planar. For a plane wavefront, amplitude remains constant, therefore intensity remains constant.


When the source of a travelling wave is linear, the wavefronts are cylindrical in shape. All the points are equidistant from the source.

In this case, amplitude of a wave, $A\propto \frac{1}{\sqrt{r}}$.
Intensity of the wave, $I\propto \frac{1}{r}$

When the source of a travelling wave is a point source, the wavefronts are spherical in shape. All the points are equidistant from the source.

In spherical wavefront,
Amplitude of a wave , $A\propto \frac{1}{r}$​
Intensity of the wave, $I\propto \frac{1}{r^2}$

Since, all the points on the spherical surface are equidistant from a point source, total intensity is independent of time.
Hence, all options are correct.