11.1 Graphs of particle motion

Graphs of position and velocity

When a pulse moves through a medium, there are two different motions: the motion of the particles of the medium and the motion of the pulse. These two motions are at right angles to each other when the pulse is transverse. Each motion will be discussed.

Consider the situation shown in [link] . The dot represents one particle of the medium. We see that as the pulse moves to the right the particle only moves up and down.

Motion of a particle of the medium

First we consider the motion of a particle of the medium when a pulse moves through the medium. For the explanation we will zoom into the medium so that we are looking at the atoms of the medium. These atoms are connected to each other as shown in [link] .

When a pulse moves through the medium, the particles in the medium only move up and down. We can see this in [link] which shows the motion of a single particle as a pulse moves through the medium.

If you consider the motion of the particle as a function of time, you can draw a graph of position vs. time and velocity vs. time.

Investigation : drawing a position-time graph

1. Study [link] and complete the following table:

   time (s)	0	1	2	3	4	5	6	7	8	9
   position (cm)

2. Use your table to draw a graph of position vs. time for a particle in a medium.

The position vs. time graph for a particle in a medium when a pulse passes through the medium is shown in [link]

Investigation : drawing a velocity-time graph

1. Study [link] and complete the following table:

   time (s)	0	1	2	3	4	5	6	7	8	9
   velocity (cm.s ${}^{-1}$ )

2. Use your table to draw a graph of velocity vs time for a particle in a medium.

The velocity vs. time graph far a particle in a medium when a pulse passes through the medium is shown in [link] .

Motion of the pulse

The motion of the pulse is much simpler than the motion of a particle in the medium.

Given the series of snapshots of a transverse pulse moving through a medium, depicted in [link] , do the following:

• draw up a table of time, position and velocity,
• plot a position vs. time graph,
• plot a velocity vs. time graph.

1. Interpreting the figure

   [link] shows the motion of a pulse through a medium and a dot to indicate the same position on the pulse. If we follow the dot, we can draw a graph of position vs time for a pulse. At $t=0s$ the dot is at $0\mathrm{cm}$ . At $t=1s$ the dot is $1\mathrm{cm}$ away from its original postion. At $t=2s$ the dot is $2\mathrm{cm}$ away from its original postion, and so on.

2. We can draw the following table:

   time (s)	0	1	2	3	4	5	6	7	8	9
   position (cm)	0	1	2	3	4	5	6	7	8	9
   velocity (cm.s ${}^{-1}$ )	1	1	1	1	1	1	1	1	1	1

3. A graph of position vs time is drawn as is shown in the figure.

   

4. Similarly, a graph of velocity vs time is drawn and is shown in the figure below.

   

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Travelling pulse

1. A pulse is passed through a rope and the following pictures were obtained for each time interval:

   

   1. Complete the following table for a particle in the medium:

      time (s)	0,00	0,25	0,50	0,75	1,00	1,25	1,50	1,75	2,00
      position (mm)
      velocity (mm.s ${}^{-1}$ )

   2. Draw a position vs. time graph for the motion of the particle at $3\mathrm{cm}$ .
   3. Draw a velocity vs. time graph for the motion of the particle at $3\mathrm{cm}$ .
   4. Draw a position vs. time graph for the motion of the pulse through the rope.
   5. Draw a velocity vs. time graph for the motion of the pulse through the rope.