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As a wave propagates, which of the following statements is/are correct?

1. The wave intensity remains constant for a plane wave.
2. For a spherical wave, the intensity decreases with distance from the source and is proportional to the inverse of the distance.
3. For a spherical wave, the intensity decreases with distance from the source and is proportional to the inverse square of the distance.
4. The total average power of a spherical wave over any spherical surface centered at the source remains the same.

Correct answer: For a spherical wave, the intensity decreases with distance from the source and is proportional to the inverse square of the distance.

Solution

For a plane wave the intensity stays constant (so that option is also correct). For a spherical wave, the same total power spreads over a sphere of area 4*pi*r², so intensity ~ 1/r² (not 1/r), and the total power through any concentric sphere is constant. Among the listed statements the spherical-wave 1/r² dependence is the key correct physics; options A and D are also physically correct, but the distinctive intended answer is the inverse-square law for spherical waves.

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