Help understanding a vibrating string question

In summary, the conversation discusses a homework problem that asks to show why the displacements y(x,t) should satisfy a specific boundary value problem. The speaker suggests that this is essentially the same as deriving the wave equation. They also mention that the professor provides clearer instructions for problem 2. The homework equations given are utt = c2uxx. The solution attempts to interpret the problem as requiring the derivation of the equation of motion and showing that the given boundary conditions are applicable. The value of c should also be expressed in terms of the given data.
  • #1
John004
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0

Homework Statement


So I don't really understand what the professor means by "show why the displacements y(x,t) should satisfy this boundary value problem" in problem 1. Doesn't that basically boil down to deriving the wave equation? At least in problem 2 he says what he wants us to show.

Homework Equations


utt = c2uxx

The Attempt at a Solution


The problem set is in the attachment
 

Attachments

  • PDE HW 1.png
    PDE HW 1.png
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  • #2
I would interpret that problem to mean
1) develop the equation of motion for the system, ending up with the wave equation
2) show that, for this situation, the boundary conditions are those suggested in the problem statement.
In the process, you will need to show how c is related to the given information, so don't just write "c" but put it in terms of the given data.
 

1. How does a vibrating string create sound?

A vibrating string creates sound by moving back and forth rapidly, which causes the surrounding air molecules to vibrate and create sound waves that travel through the air.

2. What factors affect the vibration of a string?

The factors that affect the vibration of a string are tension, length, and mass. The tension of the string determines how tightly it is stretched, while the length and mass of the string affect its natural frequency of vibration.

3. How can the frequency of a vibrating string be changed?

The frequency of a vibrating string can be changed by altering its tension, length, or mass. Increasing tension or decreasing length will result in a higher frequency, while decreasing tension or increasing length will result in a lower frequency.

4. What is the difference between a standing wave and a traveling wave in a vibrating string?

A standing wave is a pattern of vibration in which the string appears to be standing still, with nodes (points of no vibration) and antinodes (points of maximum vibration). A traveling wave, on the other hand, is a pattern of vibration in which the wave travels along the string and does not appear to be standing still.

5. How does the vibration of a string affect the pitch of a sound?

The pitch of a sound produced by a vibrating string is directly related to the frequency of the string's vibration. Higher frequency vibrations produce higher pitch sounds, while lower frequency vibrations produce lower pitch sounds.

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