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//L) sin omegat` and energy is `E_(1)` and in another experiment its displacement is `y_(2) = A sin (2pix//L ) sin 2omegat` and energy is `E_(2)`. Then

Options

A. `E_(2)=E_(1)`
B. `E_(2)=2E_(1)`
C. `E_(2)=4E_(1)`
D. `E_(2)=16E_(1)`

Answer

C

Explanation

As, energy `prop (amplitude)^(2)(f requency)^(2)` and amplitude `A` is same in both the cases, therefore,
`Eprop (f req.)^(2)`
As freq. `(200)` in `2nd` case is twice the freq. `(omega)` in the first case, therefore, `E_(2)=4E_(1)`