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The ends of a stretched wire of length \( L \) are fixed at
\( \mathrm{P} \) \( x=0 \) and \( x=\mathrm{L} \). In one experiment the displacement

W of the wire is \( y_{1}=A \sin \left(\frac{\pi x}{L}\right) \sin \omega t \) and energy is \( E_{1} \) and in other experiment its displacement is \( y_{2}=A \sin \left(\frac{2 \pi x}{L}\right) \sin 2 \omega t \) and energy is \( E_{2} \). Then:
(1) \( E_{2}=E_{1} \)
(2) \( E_{2}=2 E_{1} \)
(3) \( E_{2}=4 E_{1} \)
(4) \( E_{2}=16 E_{1} \)
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