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Speed Of A Wave Traveling Up A String

Patrick Ford
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Hey, guys, let's do a quick example. A string is hung vertically from an anchor point. If you were to grasp the string at the bottom and shake it to produce a wave traveling up the string, what happens to the speed of the wave as it moves up the string? Okay, so we have some anger point here, a rope hanging. We grab that rope and we produce a wave on it by whipping it. So this is traveling upwards. What happens to the speed of that wave as it travels up the rope? Okay. A lot of people are probably gonna want to say it decreases right off the bat, but don't associate this with freefall motion. We know the speed of a wave on a string equals attention. Divided by the mass screen at length. The mass screen length is not changing, but the tension and the rope is okay. Tension and rope is always increasing the higher up the rope you get. Okay. The simple reason is this Imagine the rope was built up, was broken up into a bunch of chains. Chain links, right. How much tension is in the chain link? Second from the bottom. Well, all that's holding all that it's supporting is one little mg, which I'll say is the weight of a single link. So the tension is just one little mg. But what if we go? One, two, three, four, five up? Then there's four chains below it. So what's the weight? It's supporting four little MGI, so it's tension is four little MGI. Let's go. We have toe to the top of this chain link. It has one, two, three, four, five, six, seven, eight, nine. So the way that it's supporting is nine little mg. So the tension is nine little mg. So clearly the tension in the rope increases the higher you go up because there's mawr rope being supported, the higher you go up. Okay. So as the tension goes up, the speed goes up, so the speed of the wave actually increases as it goes up the rope. Okay, This is contrary to our initial sort of visceral guests that it should actually decrease on its way up like objects in free fall. Alright, guys, that wraps up this question. Thanks for watching