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Learning Introductory Physics with Activities

Paul J. Emigh, Rebecka Tumblin, Kathryn Hadley, Danielle Skinner

Section 18.5 Boundary Models

Activity 18.5.1. Wave Boundaries.

Shown below is a wave pulse that is moving toward a point of the spring that is fixed (tied down so that it cannot move), represented by a dot. Note that the right side of the image is imaginary (there is no real spring there).
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A triangular wave pulse on a horizontal spring moves to the right toward a fixed end represented by a dot.
Figure 18.5.1. A wave pulse moving toward a fixed end of a spring.
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(a)

Sketch another wave pulse on the imaginary side of the figure that has the following features:
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  1. It has the same general shape as the incident pulse.
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  2. It is mirrored (reflected over the vertical line passing through the dot).
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  3. It is inverted (reflected over the horizontal).
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  4. It is moving to the left.
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(b)

Show that, as these two pulses pass each other, the superposition of the two pulses leaves the dot fixed.
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(c)

Sketch the shape of the spring at some instant after the two pulses have completely passed each other.
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(d)

Suppose the same pulse is incident on a point of the spring that is free to move up and down, represented by the same dot.
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Sketch another wave pulse on the imaginary side of the figure that has the following features:
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  1. It has the same general shape as the incident pulse.
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  2. It is mirrored (reflected over the vertical line passing through the dot).
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  3. It is not inverted.
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  4. It is moving to the left.
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(e)

Sketch the shape of the spring at a few different instants as the pulses pass each other. What do you notice about the shape of the spring near the free end?
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(f)

Sketch the shape of the spring at some instant after the two pulses have completely passed each other.
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