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Question

As a wave propagates,

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

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, A1r.
Intensity of the wave, I1r

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 , A1r
Intensity of the wave, I1r2

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.


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