Teaching Physics with the Physics Suite

Edward F. Redish

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Pulse at a boundary

A demonstrator is holding one end of an elastic string taut but steady. The right end is attached to a wall. The string is composed of two parts: a light string connected to a heavier string as shown in the figure below. Ignore the effects of gravity in this problem. Briefly explain each of your answers.

Two taut connected strings

A. How do the tensions in the two parts of the string compare?
  1. The tensions in the two parts of the string are the same.
  2. The tension in the light part of the string is greater.
  3. The tension in the heavy part of the string is greater.
  4. There is not enough information given to decide.

B. How do the speeds of wave propagation in the two parts of the string compare?

  1. The speed of propagation is the same in the two parts of the string.
  2. The speed of propagation is greater in the light part of the string.
  3. The speed of propagation is greater in the heavy part of the string.
  4. There is not enough information given to decide.

She now moves her hand up and down once quickly, sending a single pulse down the string as shown in the figure below.

pulse on two connected strings

When her pulse reaches the heavy part of the string, what will be the effect on that part of the string?

C. After the last bit of the pulse has reached the joining point, the heavy side of the string will display
  1. No pulse at all.
  2. A pulse of greater width.
  3. A pulse of smaller width.
  4. A pulse of the same width.
  5. There is not enough information to decide.

D. How does the time it takes bits of matter on the heavy side of the string to go up and down compared to what it took the bits of matter on the light side of the string?

  1. They will move up and down faster on the heavy side of the string.
  2. They will move up and down faster on the light side of the string.
  3. They will move up and down in the same amount of time on both sides of the string.
  4. Since there is no pulse on the right, the question is meaningless.
  5. There is not enough information to decide.

A second demonstrator with an equivalent apparatus now begins to move his hand up and down in an oscillatory pattern, sending pulses down the string as shown in the figure below. When his pulses reach the heavy part of the string, pulses will appear on that part of the string.

sinusoidal wave on two joined strings

E. How will the frequency of the oscillation of the bits of matter on the heavy side of the string compare to what is was on the light side of the string?
  1. The frequency will be greater on the heavy side of the string.
  2. The frequency will be greater on the light side of the string.
  3. The frequency will be the same on both sides of the string.
  4. There is not enough information to decide.

F. How will the wavelength of the oscillation of the bits of matter on the heavy side of the string compare to what is was on the light side of the string?

  1. The wavelength will be greater on the heavy side of the string.
  2. The wavelength will be greater on the light side of the string.
  3. The wavelength will be the same on both sides of the string.
  4. There is not enough information to decide.

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