What would be the difference in a cancelled out wave, and no wave? [duplicate]

Question

Thinking about waves, superposition, fourier transforms etc, and I realized I am unsure of the difference between looking at a still lake, or me and a friend standing on each side creating perfectly out of phase waves cancelling out to make a still looking lake.

Secondly where is the energy of cancelled out waves going? If a friend and I both create waves in the lake in such a way that it looks perfectly still, where is the energy we are exerting to create these waves?

Is what I'm describing even physically possible to create?

P.S this is my first question on stackexchange so I am unsure if this question is formatted properly/appropriate.

Answer 1

If a friend and I both create waves in the lake in such a way that it looks perfectly still, where is the energy we are exerting to create these waves?

What you are describing is not physically possible. It is indeed possible for you and another person to produce waves at the same frequency and in phase. Such waves will interfere with each other. However, the interference will not be destructive everywhere. In other places the interference will be constructive and the resulting waves will have a higher amplitude than what either of you produce alone.

In the end, any regions where energy is lost due to destructive interference will unavoidably be associated with regions of constructive interference, energy going into the environment, or energy going into the sources.