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Main Question or Discussion Point
consider a pulse traveling down a stretched rope. what makes the pulse to travel in a particular direction (let say to the right) and not the other?
i m not quite understand what do you mean here. are you saying that the forces on both sides of the pulse are different? what makes it different?As AngeloG was alluding to, the forces on each side of a traveling pulse are not the same. On the leading edge, the forces accelerate the rope away from the undisturbed position; on the trailing edge, back.
Yes, if you pluck a rope somewhere other than at one of the ends, the wave will travel in both directions. It's because there's no preferred direction for the wave to travel. Furthermore, the wave equation allows for disturbances in both directions. The only reason a disturbance at one end of a string will cause a disturbance in a single direction is because the wave has nowhere to go in the other.how can i post my diagram if i have no scanner?
which program should i use to draw it? AngeloG, can you post your diagram? thank you.
oh, so if i pluck the rope anywhere (not exactly to be in the middle) but not the ends of the rope, the pulses will be in both direction? but how to explain it? what is the mechanism in it?
well, what happens if you pluck a string quickly? You make a little symmetrical dimple in it, with each little element of the string pulling on the section next to it. And that's how a transverse wave propagates.oh, so if i pluck the rope anywhere (not exactly to be in the middle) but not the ends of the rope, the pulses will be in both direction? but how to explain it? what is the mechanism in it?
Thank you for your explanation. I get some picture after reading it (although i still need time to understand it completely).The point is that dynamics in mechanical systems is described by second-order differential equations in time. This means that the "information" that is needed (the initial conditions) for the system to "know" what to do next, is of first order in time: so not only the immediate POSITION (the form of the rope) counts, but also its first derivative wrt time (the velocity of the different parts of the rope).
This is why, when you start with a STILL situation (pluck the rope) and have a first derivative wrt time implicitly set to 0, that you get a different solution, than when you consider a wave that "was already travelling" (and which has, when it takes on the same immediate position, does not have the first derivative wrt time equal to 0).
So, although the immediate position (form, f(x)) at a given time t0 can be the same, the solution can be different simply because the other half of the initial conditions needed (the first time derivative) will be different. It is this difference (which would give nevertheless the same photo of the rope at t0), which makes a travelling wave, eh, travel in a certain direction, and a plucked rope send out travelling waves in both directions.
Just like Russ_Watters say here. When the pulse is travelling to the right of a string, why is that the little element at the peak only pull the section next to it (on its right) but never pull the section before it (on its left)? How to explain it in physical view (although vanesch has explained it by methametical means that the 1st time derivatives, which is the velocity of each element, also contributes to the determining of its motion)? thank you.well, what happens if you pluck a string quickly? You make a little symmetrical dimple in it, with each little element of the string pulling on the section next to it. And that's how a transverse wave propagates.
Well, a travelling pulse, at any moment t1, will have:Thank you for your explanation. I get some picture after reading it (although i still need time to understand it completely).
However, i still wondering that what is the mechanism of a TRAVELLING pulse that make it continue to travel in a particular direction.
As I said, the deformation of the string is symmetrical. So it has to travel in both directions.Just like Russ_Watters say here. When the pulse is travelling to the right of a string, why is that the little element at the peak only pull the section next to it (on its right) but never pull the section before it (on its left)? How to explain it in physical view (although vanesch has explained it by methametical means that the 1st time derivatives, which is the velocity of each element, also contributes to the determining of its motion)? thank you.
Yes. What I meant to say was, that if the pulse is already travelling in the right direction, then if you take a specific instant t1, and you look at the dynamical situation at that moment, and consider that as the "initial conditions" for the time evolution that will follow after t1, then the relationship between "configuration" (that's f(x)) and "momentum" (the time derivative of it) in these initial conditions will be such that the pulse will simply travel on in the same direction.Thank you Vanesch. I get what you want to say. You are trying to say that, when the pulse is formed, from the general solution, f(x-vt) + g(x+vt), we know that the pulse will travel in both ways, just like russ watters has told me. However, when the pulse is travelling in one direction, the instantaneous f(x) and d/dt f(x) allow it to continue to travel in the same direction. The pattern of f(x) and d/dt f(x) would not change but they are just looked like moving with the pulse. Hence, they keep the pulse moving on that direction. Am i correct?
Yes, it is the standard wave equation, the first one in arunma's calculation.But these all only valid if we can describe the system by 2nd derivative in time, right? I m not sure what do you mean by this, is it the wave equation (d'Almbert's equation, the first equation that in arunma's calculation)? Or any other equation? Can you please tell me what is the equation? thank you.