Where Does the Energy in a Standing Wave Go?

[Mr Davis 97]

I know that for standing waves, as opposed to normal waves, there is no net transfer of energy. However where does the energy go? Imagine that I have a jump rope that is attached to the wall, and I create a standing wave pattern. To keep the standing wave pattern, I must keep supplying energy to the medium (the rope). However, there is no net transfer of energy. Does the energy just come back to my hand? Where does it go?

 

[Henryk]

Good question.
The thing is, textbook examples are usually discussing 'ideal cases'. A textbook standing wave is a superposition of two waves traveling in opposite direction and their amplitude is constant, i.e. they are not attenuated as they travel. and in this case, there is no net transfer of energy. A textbook recipe for creating a standing wave is a string rigidly attached to at both ends. The wave would perfectly reflect at the end and start traveling in the opposite direction.
Reality is not perfect. If you attach a rope to the wall and start vibrating the other end, the wave you create will be attenuated along the way due to friction. Plus, the reflection coefficient at the wall may not be exactly 100 %.

 

[Jon B]

I know that for standing waves, as opposed to normal waves, there is no net transfer of energy. However where does the energy go? Imagine that I have a jump rope that is attached to the wall, and I create a standing wave pattern. To keep the standing wave pattern, I must keep supplying energy to the medium (the rope). However, there is no net transfer of energy. Does the energy just come back to my hand? Where does it go?

Mr Davis 97,
In the case of the jump rope the energy returns to the source like an echo. You will feel it. It is "reflected" and is added to and subtracted from the energy of the source and can cause an increase in amplitude when the source is in phase with the reflected wave and cause a cancelation when the source is out of phase with the reflected wave. Synchronizing the frequency of the source wave with the reflected wave will produce a visible standing wave and there will be no wave traveling from your hand to the wall when the rate of your hand shake is synchronized with the natural characteristics of the rope. A dampening device at the tie point of the rope will absorb the energy and little or no reflected wave will be produced. It is like that in the electronic world too.
Jon B