The equation for a spherical progressive wave | vedclass

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Question

(D) For a spherical wave,the intensity $I$ is inversely proportional to the square of the distance $r$ from the source,i.e.,$I \propto \frac{1}{r^2}$.

Vedclass · Accepted Answer

$y = \frac{a}{r} \sin(\omega t - kx)$

Vedclass · Answer

(D) For a spherical wave,the intensity $I$ is inversely proportional to the square of the distance $r$ from the source,i.e.,$I \propto \frac{1}{r^2}$.Since the intensity $I$ is proportional to the square of the amplitude $a$ $(I \propto a^2)$,we have $a^2 \propto \frac{1}{r^2}$,which implies $a \propto \frac{1}{r}$.Therefore,the amplitude of a spherical wave decreases as $\frac{1}{r}$.Substituting this into the standard wave equation,the equation for a spherical progressive wave is $y = \frac{a}{r} \sin(\omega t - kr)$.

The equation for a spherical progressive wave is (where $r$ is the distance from the source):

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