# 0.3 Transverse pulses  (Page 6/6)

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## Reflection of a pulse from fixed and free ends (not in caps - included for completeness)

Let us now consider what happens to a pulse when it reaches the end of a medium. The medium can be fixed, like a rope tied to a wall, or it can be free, like a rope tied loosely to a pole.

## Investigation : reflection of a pulse from a fixed end

Tie a rope to a wall or some other object that cannot move. Create a pulse in the rope by flicking one end up and down. Observe what happens to the pulse when it reaches the wall.

When the end of the medium is fixed, for example a rope tied to a wall, a pulse reflects from the fixed end, but the pulse is inverted (i.e. it is upside-down). This is shown in [link] .

## Investigation : reflection of a pulse from a free end

Tie a rope to a pole in such a way that the rope can move up and down the pole. Create a pulse in the rope by flicking one end up and down. Observe what happens to the pulse when it reaches the pole.

When the end of the medium is free, for example a rope tied loosely to a pole, a pulse reflects from the free end, but the pulse is not inverted . This is shown in [link] . We draw the free end as a ring around the pole. The ring will move up and down the pole, while the pulse is reflected away from the pole.

The fixed and free ends that were discussed in this section are examples of boundary conditions . You will see more of boundary conditions as you progress in the Physics syllabus.

## Pulses at a boundary ii

1. A rope is tied to a tree and a single pulse is generated. What happens to the pulse as it reaches the tree? Draw a diagram to explain what happens.
2. A rope is tied to a ring that is loosely fitted around a pole. A single pulse is sent along the rope. What will happen to the pulse as it reaches the pole? Draw a diagram to explain your answer.

The following simulation will help you understand the previous examples. Choose pulse from the options (either manual, oscillate or pulse). Then click on pulse and see what happens. Change from a fixed to a free end and see what happens. Try varying the width, amplitude, damping and tension.

## Summary

• A medium is the substance or material in which a wave will move
• A pulse is a single disturbance that moves through a medium
• The amplitude of a pules is a measurement of how far the medium is displaced from rest
• Pulse speed is the distance a pulse travels per unit time
• Constructive interference is when two pulses meet and result in a bigger pulse
• Destructive interference is when two pulses meet and and result in a smaller pulse
• We can draw graphs to show the motion of a particle in the medium or to show the motion of a pulse through the medium
• When a pulse moves from a thin rope to a thick rope, the speed and pulse length decrease. The pulse will be reflected and inverted in the thin rope. The reflected pulse has the same length and speed, but a different amplitude
• When a pulse moves from a thick rope to a thin rope, the speed and pulse length increase. The pulse will be reflected in the thick rope. The reflected pulse has the same length and speed, but a different amplitude
• A pulse reaching a free end will be reflected but not inverted. A pulse reaching a fixed end will be reflected and inverted

## Exercises - transverse pulses

1. A heavy rope is flicked upwards, creating a single pulse in the rope. Make a drawing of the rope and indicate the following in your drawing:
1. The direction of motion of the pulse
2. Amplitude
3. Pulse length
4. Position of rest
2. A pulse has a speed of $2,5\phantom{\rule{2pt}{0ex}}\mathrm{m}·\mathrm{s}{}^{-1}$ . How far will it have travelled in $6\phantom{\rule{2pt}{0ex}}\mathrm{s}$ ?
3. A pulse covers a distance of $75\phantom{\rule{2pt}{0ex}}\mathrm{cm}$ in $2,5\phantom{\rule{2pt}{0ex}}\mathrm{s}$ . What is the speed of the pulse?
4. How long does it take a pulse to cover a distance of $200\phantom{\rule{2pt}{0ex}}\mathrm{mm}$ if its speed is $4\phantom{\rule{2pt}{0ex}}\mathrm{m}·\mathrm{s}{}^{-1}$ ?
5. The following position-time graph for a pulse in a slinky spring is given. Draw an accurate sketch graph of the velocity of the pulse against time.
6. The following velocity-time graph for a particle in a medium is given. Draw an accurate sketch graph of the position of the particle vs. time.
7. Describe what happens to a pulse in a slinky spring when:
1. the slinky spring is tied to a wall.
2. the slinky spring is loose, i.e. not tied to a wall.
8. The following diagrams each show two approaching pulses. Redraw the diagrams to show what type of interference takes place, and label the type of interference.
9. Two pulses, A and B, of identical shape and amplitude are simultaneously generated in two identical wires of equal mass and length. Wire A is, however, pulled tighter than wire B. Which pulse will arrive at the other end first, or will they both arrive at the same time?

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