# First Harmonic/Closed Tube/Net Transfer of Energy

Standing waves have no net transfer of energy. But, when watching simulations of the first harmonic for a closed tube, I see what looks like a transfer of energy - the particles clearly appear to move one way and then the other. How do we reconcile this motion with no net transfer of energy?

### Conservation of motion

As you have already stated, there is no net transfer of energy. The "magic" word here is transfer.

Of course the particles are moving but you can notice that at the nodes, the particles are stationary. In between the nodes, the particles move "back and forth" conserving and, in a sense "recycling" the energy they have without transferring it to the neighbouring areas. Effectively, the nodes act as rigid boundaries between adjacent areas.

Since the system in the simplest formulations is lossless, the energy in the areas between the nodes is conserved and since there is no net transfer of energy, the molecules continue to move.

Please note that in order for perfect nodes (where the amplitude is exactly zero) to be formed, the system must be lossless.

Below you can see an animation of a standing wave (source: https://www.acs.psu.edu/drussell/Demos/StandingWaves/StandingWaves.html).

### First harmonic of closed tube

Now, regarding the first harmonic (I assume you mean the fundamental or else the lowest supported mode). Pretty much the same thing happens as that described above. What may be confusing here is the fact that there is a displacement antinode at one end of the tube.

You may think that there's energy being transferred either from or to the system. Whether you follow this assumption or consider the fact that the system (tube) is isolated from the rest of the environment you can reach the same results. In the first case the amount of energy going into the system equals that leaving the system so the net energy transfer remains the same, or in the latter case, the system is isolated and there is no energy transfer due to isolation.

If you are having troubles understanding the notion of reflection at a free end I suggest you have a look at the "normal incidence" reflection topic. You can find more information in most Acoustics introductory textbooks as well as Wikipedia (https://en.wikipedia.org/wiki/Reflection_coefficient).