The ends of a stretched wire of length L are fixed at x = 0 and x = L. In one experiment, the displa

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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 y1 = A sin(πx/L) sin ωt and energy is E1 and in another experiment its displacement is y2=Asin(2πx/L) sin 2ωt and energy is E2. Then

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Sol. y1= Asin $\left\lbrack \frac{\pi x}{L} ightbrack\sin\omega t$ $y_{2} = A\sin\left\lbrack \frac{2\pi x}{L} ightbrack\sin(2\omega t)$λ = 2L λ = LEnergy per unit loop$= \frac{1}{2}µ\left( \omega^{2}A^{2} ight)\lambda$E1= 1×$\left\lbrack \frac{1}{8}µ\omega^{2}A^{2}(2L) ightbrack$$E_{2} = 2 	imes \left\lbrack \frac{1}{8}(µ\omega)^{2}A^{2}(2L) ightbrack$E2 = 4E1

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