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(A) The intensity $I$ of a wave is defined as the power $P$ per unit area $A$.For a circular wave spreading in two dimensions on the surface of water,

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$r^{-1/2}$

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(A) The intensity $I$ of a wave is defined as the power $P$ per unit area $A$.For a circular wave spreading in two dimensions on the surface of water,the area $A$ is proportional to the circumference,which is $2\pi r$.Thus,the intensity $I$ is given by $I = \frac{P}{2\pi r}$,which implies $I \propto \frac{1}{r}$.Since the intensity $I$ is proportional to the square of the amplitude $A_{amp}$ (i.e.,$I \propto A_{amp}^2$),we have $A_{amp}^2 \propto \frac{1}{r}$.Therefore,the amplitude $A_{amp}$ is proportional to $r^{-1/2}$.

$A$ stone is dropped in still water,creating a circular wave pattern that spreads outward. If $r$ is the distance from the center of this circular pattern,the amplitude of the wave is proportional to ........

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