Wave Motion 5 Question 19
19. 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 the source for a spherical wave
(c) the wave intensity decreases as the inverse square of the distance from the source for a spherical wave
(d) total intensity of the spherical wave over the spherical surface centred at the source remains constant at all times
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Solution:
- For a plane wave intensity (energy crossing per unit area per unit time) is constant at all points.
But for a spherical wave, intensity at a distance $r$ from a point source of power $P$ (energy transmitted per unit time) is given by
$$ I=\frac{P}{4 \pi r^{2}} \quad \text { or } \quad I \propto \frac{1}{r^{2}} $$
NOTE For a line source $l \propto \frac{1}{r}$ because, $l=\frac{P}{\pi r l}$
