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 experiment its displacement is \[{{y}_{2}}=A\sin (2\pi x/L)\sin 2\omega t\] 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.            \[{{E}_{2}}=16{{E}_{1}}\]