- #1

- 451

- 18

## Homework Statement

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 given by ##y=A\sin\left(\frac{\pi x}{L}\right)\sin(\omega t)## and its energy is ##E_1##. In another experiment, the displacement of wire is given by ##y=A\sin\left(\frac{2\pi x}{L}\right)\sin(2\omega t)## and its energy is ##E_2##. If ##E_2=kE_1##, find ##k## (k is a positive integer).

## Homework Equations

None

## The Attempt at a Solution

$$y=A\sin\left(\frac{\pi x}{L}\right)\sin(\omega t)=\frac{A}{2}\left[\cos\left(\frac{\pi x}{L}-\omega t\right)-\cos\left(\frac{\pi x}{L}+\omega t\right)\right]$$

The given wave is formed by two waves traveling in opposite direction with amplitudes ##\frac{A}{2}##. At ##t=0##, the two waves completely cancel out each other. Hence the energy becomes zero. Isnt ##E_1## time dependent?