End of Classical String - Boundary Condition Explained

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In summary, the boundary condition for the free end of a classical vibrating string is that the spatial derivative of the string at the end must be zero. This can be explained through free body diagrams and differential force approximations, or by considering that there is a 100% reflection of any disturbance propagating towards the end, resulting in an uninverted reflection. This boundary equation accounts for the end corrections in real strings and ensures accurate results.
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zwoodrow
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The free end of a classical vibrating string imposes the boundry condition that the spatial deriviative of the string at the end must be zero. I can hand wavingly argue this with free body diagrams and manipulate the differential force approximations but i can't come up with a terse intuitive explanation of this boundry equation. any help?
 
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Another way of getting the result is that there is a 100% reflection of any disturbance propagating toward the end, and this reflection is uninverted. When you sum the incident and reflected waves, y(x) doubles, but y'(x) cancels.

This question belongs in the Classical Physics forum.
 
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Related to End of Classical String - Boundary Condition Explained

1. What is the "end of classical string" in string theory?

The "end of classical string" refers to the boundary condition in string theory, which is a mathematical framework that attempts to reconcile the theories of general relativity and quantum mechanics. In this context, the term "end" refers to the boundaries or edges of the string, which are crucial in understanding the behavior of the string and its interactions with other objects.

2. How does the boundary condition affect the behavior of a classical string?

The boundary condition plays a significant role in determining the properties and behavior of a classical string. It sets the rules for how the string can vibrate and move at its boundaries, which in turn affects its overall shape, energy, and interactions with other strings or particles.

3. What are the different types of boundary conditions in string theory?

There are several types of boundary conditions in string theory, including open, closed, and periodic. Open boundary conditions allow the endpoints of the string to move freely, whereas closed boundary conditions fix the endpoints in place. Periodic boundary conditions impose the constraint that the string must close back on itself after a certain distance, creating a loop.

4. How do boundary conditions relate to the fundamental forces in particle physics?

The boundary conditions in string theory play a crucial role in unifying the fundamental forces of nature, including gravity, electromagnetism, and the strong and weak nuclear forces. By incorporating the boundary conditions into the equations of string theory, scientists can better understand how these forces interact at a fundamental level.

5. How do scientists study and test the boundary conditions in string theory?

Scientists use a combination of theoretical calculations and experiments to study and test the boundary conditions in string theory. This can involve simulating the behavior of strings using computer models or conducting experiments at particle accelerators to observe the effects of different boundary conditions on particles and their interactions.

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