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Jeno
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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?
Doc Al said: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.
Jeno said: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.Jeno said: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?
vanesch said: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 traveling wave, eh, travel in a certain direction, and a plucked rope send out traveling waves in both directions.
russ_watters said: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.
Jeno said: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.Jeno said:Just like Russ_Watters say here. When the pulse is traveling 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.
Jeno said: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 traveling 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?
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.
Pulse movement in a stretched rope refers to the propagation of a disturbance or wave along the length of the rope. This can occur when the rope is stretched taut and then released, causing a wave to travel from one end to the other.
Directionality in pulse movement in a stretched rope can be explored by changing the direction in which the rope is stretched or by introducing obstacles or barriers along the length of the rope. This can help to determine how the direction of the wave is affected by different factors.
The direction of pulse movement in a stretched rope can be affected by the tautness of the rope, the material and thickness of the rope, the presence of obstacles or barriers, and the force applied when stretching or releasing the rope.
The direction of pulse movement in a stretched rope is directly related to the speed of the wave. If the direction of the rope is changed, the speed of the wave will also change, and vice versa. This is because the direction of the rope affects the tension and other factors that influence the speed of the wave.
Studying pulse movement in a stretched rope can have practical applications in various fields, such as engineering, physics, and sports. It can help in understanding wave propagation and its effects on structures and materials, as well as improving techniques for sports like rock climbing and rope jumping.