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(A) When a stone is thrown into still water, it creates circular ripples. The energy $E$ of the wave is conserved as it spreads outwards.The energy of

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$r^{-1/2}$

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(A) When a stone is thrown into still water, it creates circular ripples. The energy $E$ of the wave is conserved as it spreads outwards.The energy of a circular crest of width $dr$ and amplitude $h$ is proportional to its mass and the square of its amplitude. The mass of the crest is proportional to its circumference $(2 \pi r)$ and its width $(dr)$.Thus, the energy $E$ is given by:$E \propto (2 \pi r) \cdot dr \cdot h^2$Since the total energy $E$ remains constant as the wave propagates outwards, we have:$r \cdot h^2 \approx 	ext{constant}$Therefore, $h^2 \propto \frac{1}{r}$, which implies $h \propto r^{-1/2}$.Thus, the amplitude of the wave varies as $r^{-1/2}$.

$A$ 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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