question_answer

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)            \[{{E}_{2}}=16{{E}_{1}}\]