# 0.1 Transverse waves  (Page 4/4)

 Page 4 / 4

A cork on the surface of a swimming pool bobs up and down once every second on some ripples. The ripples have a wavelength of $20\phantom{\rule{2pt}{0ex}}\mathrm{cm}$ . If the cork is $2\phantom{\rule{2pt}{0ex}}\mathrm{m}$ from the edge of the pool, how long does it take a ripple passing the cork to reach the edge?

1. We are given:

• frequency of wave: $f=1\phantom{\rule{2pt}{0ex}}\mathrm{Hz}$
• wavelength of wave: $\lambda =20\phantom{\rule{2pt}{0ex}}\mathrm{cm}$
• distance of cork from edge of pool: $D\phantom{\rule{0.166667em}{0ex}}=2\phantom{\rule{2pt}{0ex}}\mathrm{m}$

We are required to determine the time it takes for a ripple to travel between the cork and the edge of the pool.

The wavelength is not in SI units and should be converted.

2. The time taken for the ripple to reach the edge of the pool is obtained from:

$t=\frac{D}{v}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\left(\text{from}\phantom{\rule{4pt}{0ex}}v=\frac{D}{t}\right)$

We know that

$v=f·\lambda$

Therefore,

$t=\frac{D}{f·\lambda }$
3. $20\phantom{\rule{0.166667em}{0ex}}\mathrm{cm}=0,2\phantom{\rule{0.166667em}{0ex}}\mathrm{m}$
4. $\begin{array}{ccc}\hfill t& =& \frac{D}{f·\lambda }\hfill \\ & =& \frac{2\phantom{\rule{0.166667em}{0ex}}\mathrm{m}}{\left(1\phantom{\rule{0.277778em}{0ex}}\mathrm{Hz}\right)\left(0,2\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\right)}\hfill \\ & =& 10\phantom{\rule{0.166667em}{0ex}}\mathrm{s}\hfill \end{array}$
5. A ripple passing the leaf will take $10\phantom{\rule{2pt}{0ex}}\mathrm{s}$ to reach the edge of the pool.

The following video provides a summary of the concepts covered so far.

## Waves

1. When the particles of a medium move perpendicular to the direction of the wave motion, the wave is called a $.........$ wave.
2. A transverse wave is moving downwards. In what direction do the particles in the medium move?
3. Consider the diagram below and answer the questions that follow:
1. the wavelength of the wave is shown by letter .
2. the amplitude of the wave is shown by letter .
4. Draw 2 wavelengths of the following transverse waves on the same graph paper. Label all important values.
1. Wave 1: Amplitude = 1 cm, wavelength = 3 cm
2. Wave 2: Peak to trough distance (vertical) = 3 cm, peak to peak distance (horizontal) = 5 cm
5. You are given the transverse wave below. Draw the following:
1. A wave with twice the amplitude of the given wave.
2. A wave with half the amplitude of the given wave.
3. A wave travelling at the same speed with twice the frequency of the given wave.
4. A wave travelling at the same speed with half the frequency of the given wave.
5. A wave with twice the wavelength of the given wave.
6. A wave with half the wavelength of the given wave.
7. A wave travelling at the same speed with twice the period of the given wave.
8. A wave travelling at the same speed with half the period of the given wave.
6. A transverse wave travelling at the same speed with an amplitude of 5 cm has a frequency of 15 Hz. The horizontal distance from a crest to the nearest trough is measured to be 2,5 cm. Find the
1. period of the wave.
2. speed of the wave.
7. A fly flaps its wings back and forth 200 times each second. Calculate the period of a wing flap.
8. As the period of a wave increases, the frequency increases/decreases/does not change.
9. Calculate the frequency of rotation of the second hand on a clock.
10. Microwave ovens produce radiation with a frequency of 2 450 MHz (1 MHz = ${10}^{6}$  Hz) and a wavelength of 0,122 m. What is the wave speed of the radiation?
11. Study the following diagram and answer the questions:
1. Identify two sets of points that are in phase.
2. Identify two sets of points that are out of phase.
3. Identify any two points that would indicate a wavelength.
12. Tom is fishing from a pier and notices that four wave crests pass by in 8 s and estimates the distance between two successive crests is 4 m. The timing starts with the first crest and ends with the fourth. Calculate the speed of the wave.

## Summary

1. A wave is formed when a continuous number of pulses are transmitted through a medium.
2. A peak is the highest point a particle in the medium rises to.
3. A trough is the lowest point a particle in the medium sinks to.
4. In a transverse wave, the particles move perpendicular to the motion of the wave.
5. The amplitude is the maximum distance from equilibrium position to a peak (or trough), or the maximum displacement of a particle in a wave from its position of rest.
6. The wavelength ( $\lambda$ ) is the distance between any two adjacent points on a wave that are in phase. It is measured in metres.
7. The period ( $T$ ) of a wave is the time it takes a wavelength to pass a fixed point. It is measured in seconds (s).
8. The frequency ( $f$ ) of a wave is how many waves pass a point in a second. It is measured in hertz (Hz) or $\mathrm{s}{}^{-1}$ .
9. Frequency: $f=\frac{1}{T}$
10. Period: $T=\frac{1}{f}$
11. Speed: $v=f\lambda$ or $v=\frac{\lambda }{T}$ .
12. When a wave is reflected from a fixed end, the resulting wave will move back through the medium, but will be inverted. When a wave is reflected from a free end, the waves are reflected, but not inverted.

## Exercises

1. A standing wave is formed when:
1. a wave refracts due to changes in the properties of the medium
2. a wave reflects off a canyon wall and is heard shortly after it is formed
3. a wave refracts and reflects due to changes in the medium
4. two identical waves moving different directions along the same medium interfere
2. How many nodes and anti-nodes are shown in the diagram?
3. Draw a transverse wave that is reflected from a fixed end.
4. Draw a transverse wave that is reflected from a free end.
5. A wave travels along a string at a speed of $1,5\mathrm{m}·\mathrm{s}{}^{-1}$ . If the frequency of the source of the wave is 7,5 Hz, calculate:
1. the wavelength of the wave
2. the period of the wave
6. Water waves crash against a seawall around the harbour. Eight waves hit the seawall in 5 s. The distance between successive troughs is 9 m. The height of the waveform trough to crest is 1,5 m.
1. How many complete waves are indicated in the sketch?
2. Write down the letters that indicate any TWO points that are:
1. in phase
2. out of phase
3. Represent ONE wavelength.
3. Calculate the amplitude of the wave.
4. Show that the period of the wave is 0,67 s.
5. Calculate the frequency of the waves.
6. Calculate the velocity of the waves.

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-1
Shedrak
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