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The ends of a stretched wire of length \( L \) are fixed at \( x=0 \) and \( x=L \). In one experiment, the displacement of the wire is \( y_{1}=A \sin (\pi x / L) \sin \omega t \) and energy is \( E_{1} \), and in another
\( \mathrm{P} \) experiment its displacement is \( y_{2}=A \sin (2 \pi x / L) \sin 2 \omega t \)

W and energy is \( E_{2} \). Then
[IIT-JEE (Screening) 2001]
(a) \( E_{2}=E_{1} \)
(b) \( E_{2}=2 E_{1} \)
(c) \( E_{2}=4 E_{1} \)
(d) \( E_{2}=16 E_{1} \)
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