# 0.3 Transverse pulses

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## Investigation : pulse length and amplitude

The graphs below show the positions of a pulse at different times.

Use your ruler to measure the lengths of $a$ and $p$ . Fill your answers in the table.

 Time $a$ $p$ $t=0$  s $t=1$  s $t=2$  s $t=3$  s

What do you notice about the values of $a$ and $p$ ?

In the activity, we found that the values for how high the pulse ( $a$ ) is and how wide the pulse ( $p$ ) is the same at different times. Pulse length and amplitude are two important quantities of a pulse.

## Pulse speed

Pulse Speed

Pulse speed is the distance a pulse travels per unit time.

In Motion in one dimension we saw that speed was defined as the distance traveled per unit time. We can use the same definition of speed to calculate how fast a pulse travels. If the pulse travels a distance $D$ in a time $t$ , then the pulse speed $v$ is:

$v=\frac{D}{t}$

A pulse covers a distance of $2\phantom{\rule{3pt}{0ex}}\mathrm{m}$ in $4\phantom{\rule{3pt}{0ex}}\mathrm{s}$ on a heavy rope. Calculate the pulse speed.

1. We are given:

• the distance travelled by the pulse: $D=2\phantom{\rule{2pt}{0ex}}\mathrm{m}$
• the time taken to travel $2\phantom{\rule{2pt}{0ex}}\mathrm{m}$ : $t=4\phantom{\rule{2pt}{0ex}}\mathrm{s}$

We are required to calculate the speed of the pulse.

2. We can use:

$v=\frac{D}{t}$

to calculate the speed of the pulse.

3. $\begin{array}{ccc}\hfill v& =& \frac{D}{t}\hfill \\ & =& \frac{2\phantom{\rule{0.166667em}{0ex}}\mathrm{m}}{4\phantom{\rule{0.166667em}{0ex}}\mathrm{s}}\hfill \\ & =& 0,5\phantom{\rule{0.166667em}{0ex}}\mathrm{m}·{\mathrm{s}}^{-1}\hfill \end{array}$
4. The pulse speed is $0,5\phantom{\rule{2pt}{0ex}}\mathrm{m}·\mathrm{s}{}^{-1}$ .

The pulse speed depends on the properties of the medium and not on the amplitude or pulse length of the pulse.

## Pulse speed

1. A pulse covers a distance of $5\phantom{\rule{2pt}{0ex}}\mathrm{m}$ in $15\phantom{\rule{2pt}{0ex}}\mathrm{s}$ . Calculate the speed of the pulse.
2. A pulse has a speed of $5\phantom{\rule{2pt}{0ex}}\mathrm{cm}·\mathrm{s}{}^{-1}$ . How far does it travel in $2,5\phantom{\rule{2pt}{0ex}}\mathrm{s}$ ?
3. A pulse has a speed of $0,5\phantom{\rule{2pt}{0ex}}\mathrm{m}·\mathrm{s}{}^{-1}$ . How long does it take to cover a distance of $25\phantom{\rule{2pt}{0ex}}\mathrm{cm}$ ?
4. How long will it take a pulse moving at $0,25\phantom{\rule{2pt}{0ex}}\mathrm{m}·\mathrm{s}{}^{-1}$ to travel a distance of $20\phantom{\rule{2pt}{0ex}}\mathrm{m}$ ?
5. The diagram shows two pulses in the same medium. Which has the higher speed? Explain your answer.

## Superposition of pulses

Two or more pulses can pass through the same medium at that same time in the same place. When they do they interact with each other to form a different disturbance at that point. The resulting pulse is obtained by using the principle of superposition . The principle of superposition states that the effect of the different pulses is the sum of their individual effects. After pulses pass through each other, each pulse continues along its original direction of travel, and their original amplitudes remain unchanged.

Constructive interference takes place when two pulses meet each other to create a larger pulse. The amplitude of the resulting pulse is the sum of the amplitudes of the two initial pulses. This is shown in [link] .

Constructive interference
Constructive interference is when two pulses meet, resulting in a bigger pulse.

Destructive interference takes place when two pulses meet and cancel each other. The amplitude of the resulting pulse is the sum of the amplitudes of the two initial pulses, but the one amplitude will be a negative number. This is shown in [link] . In general, amplitudes of individual pulses add together to give the amplitude of the resultant pulse.

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