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

Answer

C

Explanation

Energy `prop ("amplitude")^(2) ("frequency")^(2)`
Amplitude (A) is same in both the cases, but frequency `2omega`, in the second case is two times the frequency `(omega)` in the first case,
`E_(2) = 4E_(1)`