The ends of stretched wire of length $L$ are fixed at $x\, = 0$ and $x \,= L$. In one experiment, the displacement of the wire is ${y_1} = A\sin\, \left( {\pi x/L} \right)\sin \,\omega t$ and energy is $E_1$. and in another experiment its displacement is ${y_2} = A\sin \,\left( {2\pi x/L} \right)\sin 2\omega t$ and energy is $E_2$, Then
Medium
$(Amplitude)^2\, (Frequency)^2$ Amplitude is same in both the cases, but frequency $2\omega$ in the second case is two times the frequency $(\omega)$ in the first case, Hence $E_2\, = 4E_1$
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