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I am having a hard time visualizing how energy can be transmitted at a node of a standing wave. Basically, how can an immobile point be pulling on its neighboring points, without being in motion itself?

Let's take a simple case. Imagine a "rope" composed of single atoms, where one atom is connected on the left to exactly one atom, and to exactly to another atom on the right.

When the middle atom is pushed down, since it is has bonds to the neigboring atoms, it drags these neighbors down. This is visually manifested as a wave. For simplicity's sake, let's follow this wave in one direction (to the right only, for example). This middle atoms pulls on neighbor # 1, which pulls on neighbor # 2, and so on. The wave propagates. The original middle atom eventually loses kinetic energy, or is pulled back towards equilibrium/center, and returns to it's original spot.

But this whole phenomenon relies on the middle atom moving down and tugging on it's neighbor.

Now we go to the nodes on a standing wave. At this point, there is no movement, as this point is simultaneously exposed to forces that equally drive it up and down, therefore cancelling. So this point at the node does not move. And yet, it's neighbors will get pulled: for example, the neighbor on the left will get pulled up, and the neighbor on the right will get pulled down, SIMULTANEOUSLY!

I am sure I am missing a fundamental concept here, but it is very counterintuitive to me. For example, I get how in Newton's third law, the action-reaction force pairs do not cancel because they are acting on different objects. But transmittance at the node continues to elude me.

Can anyone explain this to me (or point me to a high-yield post where this is explained in simple terms)?