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 y1=Asin (πxL)sin ωt and energy is E1, and in another experiment its displacement is y2=Asin(2πxL)sin 2ωt and energy is E2. Then
E2=4E1
Energy(E)∝(Amplitude)2 (Frequency)2
Amplitude is same in both the cases, but frquency 2ω in the second case is two times the frequency (ω) in the first case.
Hence E2=4E1