\[\Delta m=\rho\Delta V=\rho S\Delta x\]

\[\Delta E_k=\frac{1}{2}v^2\Delta m\]

\[v=\frac{\partial y}{\partial t}=-A\omega\sin\left[\omega\left(t-\frac{x}{u}\right)+\varphi\right]\]

\[\therefore\ \Delta E_k=\frac{1}{2}v^2\Delta m=\frac{1}{2}\rho A^2\omega^2\sin^2\left[\omega\left(t-\frac{x}{u}\right)+\varphi\right]\Delta V\]