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(C) The energy $E$ of a standing wave is proportional to the square of the amplitude $(A)$ and the square of the angular frequency $(\omega)$.Mathemat

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$E_2 = 4E_1$

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(C) The energy $E$ of a standing wave is proportional to the square of the amplitude $(A)$ and the square of the angular frequency $(\omega)$.Mathematically,$E \propto A^2 \omega^2$.In the first case,the displacement is $y_1 = A \sin(\pi x/L) \sin(\omega t)$,so the amplitude is $A$ and the angular frequency is $\omega$. Thus,$E_1 = k A^2 \omega^2$ (where $k$ is a constant).In the second case,the displacement is $y_2 = A \sin(2\pi x/L) \sin(2\omega t)$,so the amplitude is $A$ and the angular frequency is $2\omega$.Thus,$E_2 = k A^2 (2\omega)^2 = k A^2 (4\omega^2) = 4(k A^2 \omega^2)$.Comparing the two,we get $E_2 = 4E_1$.

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