Suppose you have a taut string, and you pinch it firmly at the middle, so that the middle is immobile but the string has the same tension throughout. Then you start vibrating one end of the string. I would think that the wave could not propagate past the middle of the string, because you have fixed that point. The second half of the string won't move for that reason. So instead, you stop pinching the string, and allow the vibrations to occur at such a frequency as to activate the second mode of oscillation of your string. With this mode in action, you once again pinch the string in the middle. The standing wave will continue uninterrupted, because this point was a node - it was fixed anyway. This is a very unintuitive result to me. I would intuitively think that pinching the string would somehow isolate the two halves from one another, and make it impossible for energy to be supplied from the initial end to affect the opposite end, but this is not so. The best explanation that has come to me is that, although the displacement and velocity of the infinitesimal pinched segment is held to be zero, its tension oscillates, and this enables energy to be transmitted through it. Is this the explanation, or is there something else to it?