Questions tagged [string]

This tag is for non-relativistic material strings, such as, e.g., a guitar string. PLEASE DO NOT USE THIS TAG for relativistic strings and string theory.

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Euler-Lagrange equations for chain fountain

Most of us are familiar with chain fountains. I was wondering how this phenomenon is explained in the Lagrangian mechanics. I mean do we know how the Euler-Lagrange equations look like for this system?...
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5 votes
1 answer
75 views

Deriving wave equation of string without approximation

When deriving the equation for a standing wave of a string, we often approximate that the tension at all points in the wave is constant. but I want to derive the equation without the approximation. I ...
4 votes
1 answer
33 views

Does rope in a standing wave expand and contract as it moves between being straight vs sine?

Images of standing waves often show two people using a jump rope. The shape of the rope goes from straight to waves to straight, then a sine wave the other way and then straight again as it repeats. ...
4 votes
0 answers
84 views

Prove from first principles that a guitar string will vibrate at a constant frequency

From experience I am aware that a taught string will generally vibrate with a constant frequency. I wanted to prove this by considering the relation of distance from the resting position, and its ...
4 votes
0 answers
176 views

Polyakov action as broken symmetry effective action

I would like to ask if it is possible to regard the Polyakov action as an effective action that describes the broken symmetric phase of a more general model. Could someone draw an analogy with O(N) ...
4 votes
2 answers
2k views

How can one conclude upward force is related to tension in this question?

In preparation for the SAT Physics Subject Test, I have been doing extra practice problems. This one states: A garment bag hangs from a clothesline. The tension in the clothesline is $10 \,\text{N}$...
3 votes
0 answers
31 views

Singularities in gauge-fixing conditions and topological defects

I am studying the 't Hooft's paper "Topology-of-the-gauge-condition-and-new-confinement" https://doi.org/10.1016/0550-3213(81)90442-9 and there are several points which I would like to ...
3 votes
1 answer
82 views

String conservation with springs

I was trying to solve this Problem that asked to find the period of small oscillations for this system. To do so I used the fact that for a massless pulley with strings around it, the sum of the ...
3 votes
0 answers
183 views

Analysis of motion of a body moving on a string?

I was wondering about something I observed yesterday. To give some background, one of my hobbies is slacklining. This is essentially like tight-rope walking but with a one inch piece of (in this case ...
3 votes
2 answers
4k views

Neglecting friction on a pulley?

So, this is how the problem looks: Plus, the pulley is suspended on a cord at its center and hanging from the ceiling. You're given masses of the objects, mass of the pulley and it's radius. And your ...
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2 votes
1 answer
84 views

Determining the equations of motion for a 2 DOF in 2 directions

I'm having trouble understanding a 2DOF system that moves in 2 directions. The problem asks me to determine the EOM for a system shown in the attached image: My first idea is to transform this system ...
2 votes
0 answers
86 views

Taut strings in curved spacetime

In general relativity, a straight line is defined (or, in a sense, replaced?) by the path a light beam takes. In Newtonian physics, another way to approximate a straight line between two points is to ...
2 votes
0 answers
72 views

Why does a violin sound louder when I bow faster?

When you bow a violin string, the string vibrates at a specific frequency. It sounds louder when you bow faster - that is when the string stick and slip against the bow with larger displacement (or ...
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2 votes
4 answers
172 views

Tension in massless rope

We are learning Newton laws in the University and were given the following problem: In the system described in the image, the man is pulling two massless ropes with a force of $F$ each. We are ...
2 votes
2 answers
169 views

Implications of massless pulleys in Atwood machines

Consider the double Atwood machine below: I understand the classic approach to a solution for the acceleration of each mass involves setting the tension in the upper string equal to twice that of the ...
2 votes
3 answers
543 views

Can you determine an action-reaction pair when tension acts on a string attached to a pulley?

I have been learning about tension and was doing some reading on trying to explain these forces at the intermolecular level and later also trying to see how it fits in view of Newton's third law- I ...
2 votes
0 answers
182 views

How long does it take for a wave pulse on a string to get reflected from rigid boundary?

This question arises from analysis of standing waves.The incident wave has the equation $$y=Asin(kx-\omega t)$$The reflected wave has the equation$$y=Asin(kx+\omega t +\pi)$$When determining the ...
2 votes
2 answers
384 views

Amplitude of a wave, and boundary effects

I am curious as to what causes a discrepancy in the amplitude between the incident and the reflected/transmitted pulse. (* For instance, in the first image, the incident pulse seems to be of greater ...
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2 votes
1 answer
430 views

Extensible string on a pulley

Suppose we have an extensible massless string satisfying Hooke's Law, tied to a wall at one end and going over a 'frictional pulley'. Now if we tie the other end with a mass $M$, the total length of ...
2 votes
1 answer
308 views

Capstan equation with only one end of rope under tension

The capstan equation will give me the relation between the tension force at both sides of a rope wrapped around a cylindrical object, but what happens in this situation where the 'rope' is something ...
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2 votes
0 answers
136 views

Deriving the longitudinal sound wave from the transverse string vibration

I am trying to derive the longitudinal sound wave (i.e. either the pressure $\psi_P(x,t)$ or the displacement $\psi(x,t)$, where both $\psi$s are in the direction of $x$) produced by the vibrations of ...
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2 votes
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36 views

Trying to prove, that an initial spatial and restricted displacement on an infinite string, with a density discontinuity, will transmit AND reflect

This is a rather trivia problem, but I have been trying to prove it, since all of the Books I have read - online or not - take it for granted. The problem I'm talking about is "Vibration of String" ...
2 votes
0 answers
378 views

Extension of the Capstan Equation

The Capstan Equation relates the holding force and the load force for a string wrapped around a cylinder. However, most people who work with heavy machinery know that if you wrap a rope around a post ...
2 votes
0 answers
99 views

Corresponding conservation law to Lagrangian symmetry

Using this Lagrangian : $L=\frac{1}{2}\left(u_t^2-u_x^2\right)$, which describes a simple string. I know about these vector fields which are the symmetries of this Lagrangian $$\frac{\partial}{\...
2 votes
0 answers
704 views

Standing Waves in a String of two Linear Densities

Given a string with sections of two linear densities like this: Does the point where the two linear densities meet have to be a node if a standing wave is produced? Are there alternatives? Could I ...
2 votes
0 answers
150 views

Speed of breaking (guitar) string

As I was playing the guitar yesterday, one of the strings broke and injured one of my fingers lightly. Astonished by the power of a breaking string, I was wondering whether there is a way to ...
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21 views

Circular motion after tension gets zero

If we have an object rotating in a vertical plane, with a cord which cannot extend (has fixed length), what happens after the tension goes to zero? How do I prove mathematically that the trajectory ...
1 vote
1 answer
55 views

Catenary curved string with differing linear densities - Linear density distribution

Do you guys know if there's some kind of weight distribution that fits a problem like this one? Let there be a string with two different sections with different linear densities, like the following ...
1 vote
2 answers
75 views

Why is the potential energy of a suspended rope proportional to the stretch?

In A. Zee Einstein Gravity in a Nutshell, when he is talking about variational calculus on page 113, he gives an example of a suspended rope. To calculate the total potential energy due to tension, it'...
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1 vote
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54 views

Is it possible to find Tensional force from Lagrangian?

The Lagrangian principle is easier to solve than any kind of problem. But, we always "forget" (not really, but we don't take it into account directly), of Tension in a system when looking at ...
1 vote
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15 views

String vibration under periodic boundry conditions

I wish to known which are the vibration modes (in case that they exist) of an string vibrating under periodical boundary conditions (PBC). The question is related to molecular dynamics simulations of ...
1 vote
0 answers
63 views

Tension in a stretched string

I am working my way through Alistair Rae and Jim Napolitano's Quantum Mechanics textbook (sixth edition). In the introductory section, the example of a stretched string is used to derive the wave ...
1 vote
0 answers
35 views

The effect of a temperature change on the fundamental frequency of a stretched string

I am curious about the effect of temperature on the frequency of say, a guitar string (stretched under a tension $F_T$ and of fixed length $L$). I wonder if someone here could check my work. First of ...
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1 vote
1 answer
65 views

Question about fundamental frequencies

For a string fixed at both ends, with a fundamental frequency of 440Hz, can there be a harmonic when a wave of frequency 220Hz is sent across the string? my book says no, but I disagree; can't ...
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33 views

Is there a relation between eigenvector and amplitude for a beaded string

I have a string fixed at both end with 5 beads. At $$t=0$$ $$v_p=0$$ where $p$ is the index for each bead and their initial displacement are $$(3,0,\sqrt{3},2,2)$$ I have to find the amplitude for the ...
1 vote
1 answer
132 views

Linear wave superposition along a rope/string

This question basically roots to fundamentals of waves which is quite difficult for me to visualize. Hope that I can clear out this confusion based on answers to this question Would be grateful if ...
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1 vote
0 answers
39 views

How is tension act microscopically in a string?

Think of a massless string that goes through two pulleys attached to a roof, also massless, and look at this scenario as if you were seeing the string in its atomic constitution, looking at the parts ...
1 vote
1 answer
141 views

Potential Energy for Non-conservative Forces

I was studying for the GRE and came across the problem below. A small puck of mass $M$ is attached to a massless string that drops through a hole in a platform, as shown in the diagram above. The ...
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1 vote
2 answers
429 views

Question regarding tug-of-war and tension

I am having a hard time understanding these questions regarding tension$-$ Is the tension in a rope uniform in a tug of war? If yes, then who wins the game? If no, doesn't that violate Newton's ...
1 vote
2 answers
358 views

What if we used extensible string in pulley?

While I was solving questions,I saw that in most the questions, it's written that the used string in pulley is non-extensible, Why? What would happen if we used extensible string having elasticity?
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1 vote
1 answer
158 views

Equivalent length of a simple pendulum

i was solving some question based on harmonic oscillations and a question popped up: If the angle between the the wires and the surface is 45 and the mass of the bob is $m$ calculate the time period ...
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1 vote
0 answers
26 views

Reason for wave inversion on a string with 2 media?

This question has been partially addressed here. I use it while stating that Newton's 3rd Law and the action of tension on a string explain why a wave is inverted on encountering a fixed end. But I ...
1 vote
1 answer
53 views

Foucault pendulum: diagnosing experimental systematics

I did the Foucault pendulum experiment today. I used a 45 pound weight hung on about 12 or 15 feet of inelastic cord. I understand that a great and highly precise experiment will show one full ...
1 vote
1 answer
35 views

Tension on a massless string holding a semisphere in place

I am having trouble solving this. The problem is the following: Suppose a semisphere of radius $a$ (with its center of mass at $h = \frac{3}{8}a$) of mass $m$ located on a sliding surface. A massless,...
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1 vote
0 answers
68 views

Limit speed of a whip in vacuum

Inspired by this answer, I want to ask what is going to limit the speed of the tip of a whip in a vacuum? From my understanding, on Earth the tip reaches speeds only several times bigger than the ...
1 vote
1 answer
66 views

Variational problem for strings

I'm working through Zwiebach's String theory book by myself and I'm having trouble starting problem 4.7. For those that do not have a copy, I'll paraphrase the question: A string is stretched from $x=...
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1 vote
1 answer
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Tension in string involved in multiple Atwood machines and how is it different in different situations

Consider the 2 situations shown in the figure In situation 2, it's quite obvious that T/2 is proportional to g. But, what I've come to know about situations like situation 1(here) is that- this ...
1 vote
0 answers
28 views

Mechanical wave transmission through 3 strings of different medium qualities

How would the motion of waves behave if there are 3 strings joined to each other (as displayed in the fig.) and a wave was started in the string-3? Which would undergo inversion of strings and for ...
1 vote
2 answers
85 views

Why doesn't the block fall?

I came upon this question as I was going through the concepts of tension. Well according to Newton's third law- every action has an equal and opposite reaction. Here my question is that if the tension ...
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1 vote
0 answers
70 views

For wave functions $y(x, t)$, how the second order partial differentiation works as second order absolute differentiation?

Ref: http://www.animations.physics.unsw.edu.au/jw/wave_equation_speed.htm As far as we've defined wave as the disturbance caused due to Force obeying Hooke's Law. So, the derivation was started with ...
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