## Lecture (12 minutes)

Notes on energy density in waves energy_wiki.ppt

Discuss the concept of energy density, which is more relevant for a continuum system. There is energy transmitted when a harmonic wave propagates in a rope. What is its origin? The kinetic energy in a rope comes from its motion, of course, but where does the potential energy come from? (It's stored in the stretch). Must then find an expression for how much the rope is stretched at each point. $\ell -\Delta x\approx \frac{1}{2}\left[ \frac{\Delta \psi }{\Delta x} \right]^{2}\Delta x$

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• $W(x,t)=\frac{Z}{2v}\left[ \left( \frac{\partial \psi (x,t)}{\partial t} \right)^{2}+v^{2}\left( \frac{\partial \psi (x,t)}{\partial x} \right)^{2} \right]$

Some discussion can follow, but the activity following generates all the necessary discussion. Students work in groups discussing the energy density (kinetic, potential, total) at different places and times in both traveling and standing waves, and then discuss the transfer of energy.

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