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(B) The energy per unit time intercepted by a surface is given by the power $P$,which is proportional to the intensity $I$ and the area $S$. Since int

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$2E$

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(B) The energy per unit time intercepted by a surface is given by the power $P$,which is proportional to the intensity $I$ and the area $S$. Since intensity $I \propto A^2$,where $A$ is the amplitude,the power intercepted is $P \propto A^2 S$. Let the initial power be $P_1 = E = k A^2 S$,where $k$ is a constant. For the new conditions,the new area is $S' = \frac{1}{2} S$ and the new amplitude is $A' = 2A$. The new power $P_2$ is given by $P_2 = k (A')^2 S' = k (2A)^2 (\frac{1}{2} S)$. $P_2 = k (4A^2) (\frac{1}{2} S) = 2 k A^2 S$. Since $E = k A^2 S$,we have $P_2 = 2E$.

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