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A stone thrown into still water, creates a circular wave pattern moving radially outwards. If $r$ is the distance measured from the centre of the pattern, the amplitude of the wave varies as
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$r^{-1 / 2}$
For circular wave, intensity $I \propto \frac{1}{r}$.
Amplitude, $A \propto \sqrt{I}, A \propto \sqrt{\frac{1}{r}}$ or, $A \propto r^{-1 / 2}$.
Amplitude, $A \propto \sqrt{I}, A \propto \sqrt{\frac{1}{r}}$ or, $A \propto r^{-1 / 2}$.
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