Physics
Cambridge IGCSE

TOPIC 3: WAVES

# 3.1 Wave properties

In this section we will learn about the fundamental properties of waves, including how they are measured. We will also learn about some key differences between types of waves, and how waves can be investigated through some simple experiments.

## What is a wave?

In science, a wave is any oscillation or vibration that transfers energy. For example, in a water wave, the molecules of water on the surface of a lake oscillate up and down whilst a water wave moves across the lake. The wave carries energy across the lake, and can make boats move far away from the source of the wave. Note that the water does not move across the surface of the lake, just the wave energy.

The most common forms of waves that you will learn about in this course include light (and other electromagnetic waves - see section 3.3), sound, water waves and waves on wires, ropes and springs.
Waves can be used to transfer information as well as energy. This is a vital feature of our use of electromagnetic waves in communication.

## Measuring waves

Figure 1 shows a diagram of a wave. It could be a sound wave or any other type of wave, but let us first look at water waves, as we are all familiar with these.

Figure 1. Diagram of a water wave

As you can see in the diagram, some measurements have been added. Here is a list of all of the most common measurements made for waves:

1. Wavelength (λ) - this is the distance from the wave peak to the next peak (or the 'trough' to the next trough). It is measured in metres (m). Note that wavelength is given a Greek letter symbol λ, called 'lambda'. (see figure 1).

2. Amplitude - this is the height of a wave form the peak to the central line. For a water wave, it it the height of the wave compared to the flat surface of the water. It is typically measured in metres (m) for waves like water waves. Note there is no standard symbol for amplitude at GCSE level, but 'A' is often used. (see figure 1). The higher the amplitude, the more energy is transferred. Therefore, a high amplitude light wave will be very bright, and a high amplitude sound wave will be very loud.

Here are some other standard wave measurements, not shown on figure 1:

3. Frequency (ƒ) - the number of waves produced per second (or past a point per second). The unit for frequency is hertz (Hz). Therefore, if 20 water waves are produced every 2 seconds, that gives 10 waves per second, or a frequency of 10 Hz.

4. Time period (T) - this is simply the time for a single wave or oscillation. For water waves, this would be the time for the water to move down then back up again to the top of the wave. The time period is measured in seconds.

5. Wave velocity (v) - as the name implies, this is the velocity (or speed) of the wave. It is measured in meters per second (m/s).

All of the five measurements listed above are used frequently in the waves topic, so you should know what they mean and how they are measured. In section 3.2, we will look at how the measurements are linked with some basic formulas.

## Wavefronts

A wavefront is defined - in simple terms - as a line joining all points at the same position in the oscillation of the wave. This is often taken to be all the points at the peak of a wave. In figure 2, you can clearly see this ocean wavefront - it makes a long line at the top (or crest) of the wave.

Figure 2. A water wavefront

As you can see from figure 2, the wavefront is perpendicular (900) to the direction of wave motion. This is true for just about all waves, including light and sound waves. We will meet wavefronts later on in some wave diagrams involving light waves and water waves in a ripple tank.

## Longitudinal and transverse waves

If you watch a ball in a swimming pool as a wave goes past from left to right, the ball clearly moves up and down. This is because the water at the surface always moves up and down as the wave moves sideways. Any wave where the particles (or 'disturbance') oscillate perpendicular (at right angles) to the direction of wave motion is called a transverse wave.

Transverse waves include all electromagnetic waves (for example light), water surface waves and waves in wires - for example on a guitar. A 'Mexican wave' in a sports stadium is a transverse wave because people move up and down as the wave travels sideways. The disturbance is perpendicular to the wave direction of motion

A longitudinal wave is different - the oscillation of particles is parallel to the wave motion. The most common example of this is a sound wave. Sound waves in air cause the air molecules to vibrate backwards and forwards, parallel to the direction of the sound wave.

Springs can be used to demonstrate both longitudinal and transverse waves, as shown in this video. it also helps to visualise what is happening. Watch the individual coils on the spring as the waves move past.

YouTube - Longitudinal and transverse waves on a spring

Note that on the longitudinal wave shown in this video, the spring coils get pushed together, or compressed, in some regions. At other points the coils are further apart, and this is called a rarefaction, as shown in figure 3 below. Compressions and rarefactions are found in all longitudinal waves like sound waves and the waves on a spring shown here.

Figure 3. Compressions and rarefactions

### Summary

Transverse Waves:

• Electromagnetic waves (like light)
• Water surface waves
• Waves on wires/strings (e.g. musical instruments like guitars)
• Seismic S-waves (see below)

Longitudinal Waves:

• Sound waves
• Seismic P-waves (see below)
• S-waves

Note that springs can make both longitudinal and transverse waves as shown in the video above.

## Seismic waves

Seismic waves are waves in the Earth produced by earthquakes. An earthquake can be devastating, but smaller earthquakes happen regularly and produce waves that travel through the Earth. We now know that there are several different types of waves that can be produced:

1. P-waves.
These are longitudinal waves. As with all longitudinal waves, they can travel through liquids and solids, and are 'compression' waves causing regions of compression and rarefaction. They travel faster than S-waves through the Earth.

2. S-waves
These are transverse waves. They can only travel through solids. Normally, transverse waves can exist on the surface of liquids, but S-waves travel through the Earth, and as they are transverse they cannot pass through any liquids. S-waves travel at a slower speed than P-waves, hence the name: The 'S' stands for secondary waves.

Seismic waves can be detected with sensitive seismometers, and theses have been placed all around the Earth. They led to an amazing discovery in 1936 by a Danish geologist called Inge Lehmann. She discovered that the Earth has a solid central core within an outer liquid core. In certain parts of the Earth, no S-waves are detected from large earthquakes on the other side. The only possible explanation for this is that the Earth must have a large mass of liquid at some point in the centre. Using data collected after a large earthquake in New Zealand, Lehmann found evidence that there must be a solid core within the liquid core.
Her discoveries along with other findings led to the construction of a model for the Earth as shown in figure 3:

Figure 4. The hidden structure of the Earth

Note: You do not need to learn the names of these layers or about how seismic waves led to these discoveries.

Questions:

1. Ocean waves hit a wall in a harbour at a rate of 12 waves per minute. What is the frequency of these waves?

If there are 12 waves per minute, then we have 12 waves per 60 seconds.
The frequency is defined as the number of waves per second, so we need to divide 12 by 60:

 frequency = 12 60

frequency = 0.2 Hz (hertz)

2. A wave produced on a long rope is a transverse wave.

• a) Explain what is meant by a transverse wave.
• b) Give one other example of a transverse wave.
• c) Give one example of a longitudinal wave.

a) A transverse wave is where the particles/disturbance moves at 900 - perpendicularly - to the wave motion.

b) Water (surface) waves, Light (or any electromagnetic wave) are all transverse waves.

c) Sound is the most common example of a longitudinal wave.

## Wave velocity and wavelength

A rubber duck is bobbing up and down on a small puddle, producing waves as shown in figure 5 below. Two waves are made each second, so the frequency of the waves is 2 Hz. If each wave is 3 cm apart, how fast is the wave going?

Figure 5. The velocity of water waves
(Not to scale!)

If the waves have a frequency of 2 Hz, (2 per second) and the wavelength is 3 cm long as shown here, then the first wave must have travelled 6 cm to the right in the first second. It therefore has a velocity of 6 cm per second, or 6 cm/s.

This tells us that - to find the wave velocity - we simply multiply the frequency of the waves by the wavelength.
The formula is therefore:

wave velocity = frequency x wavelength

v = ƒ λ

[m/s] = [Hz] x [metres]

Learn this formula!

This formula is true for all waves, including light and sound waves.

The velocity of sound in air is about 330 m/s. For light it is about 300 000 000 m/s! (3 x 108 m/s). As you can see, the velocity of light is enormous, and much faster than sound. This is why we see a flash of lightning pretty instantaneously, but the sound wave (the thunder) takes some time to reach us, producing a delay between the 'flash' and the 'bang'.

Example:
The wavelength of one type of radio wave is 90 cm and the frequency 3.3 x 108 Hz. Calculate the speed of this wave.

The wavelength should be in metres, so λ = 0.9 m.
We know that v = ƒ x λ and so v = 3.3 x 108 x 0.9
Therefore v = 3.0 x 108 m/s
(note that this is the same as the speed of light, as both are electromagnetic waves, covered in section 3.5.)

Questions:

3. Sound waves have a velocity of 330 m/s in air. A car horn makes a sound of frequency 500 Hz.

Calculate the wavelength of the sound produced.

We know that v = ƒ x λ, so the wavelength λ is:

 λ = v ƒ
 λ = 330 500

λ = 0.66 m

4. Water waves are travelling across a pond at a speed of 2 m/s. 20 waves move past a point in 5 seconds.

• a) Calculate the frequency of the waves.
• b) State the formula linking frequency, wavelength and wave speed for the water waves.
• c) Using your answer from part (a), calculate the wavelength of the water waves.

a) We know frequency is the number of waves per second. Therefore if there are 20 waves in 5 seconds, the frequency must be 4 per second, or f = 4 Hz

b) The formula is v = ƒ λ.

c) We know that v = ƒ λ, and that v = 2 m/s, so the wavelength λ is:

 λ = v ƒ
 λ = 2 4

λ = 0.5 m.

### Time period and frequency

There is actually a mathematical link between these two measurements. If you would like to find out more, click here.

Let's go back to the duck example above in figure 5. The movement of the duck is creating 2 waves per second. This means the frequency of the waves is 2 Hz. However, if it makes 2 waves per second, then it only takes ½ second to make one wave - the time period is 0.5 s.
If the frequency of the waves was 4 per second (4 Hz) the time period would be ¼ second (0.25 s). As we can see from this, the time period of the waves is the 'reciprocal' of the frequency. Written as a formula, this gives:

 frequency (Hz) = 1 time (s)
 ƒ = 1 T

## Reflection, Refraction, Diffraction

All waves can undergo changes of direction as they travel, and the three main ways this happens are listed here:

1. Reflection - this is when any wave 'bounces' back off an object. You should have met the idea of reflection previously, and the reflection of light is covered in more detail in the next section, 3.2a.

2. Refraction - this is when a wave changes direction due to a change in speed. For example, light waves are refracted when they pass into a glass block and slow down. This is covered in more detail in section 3.2b.

3. Diffraction - this is when a wave passes through a narrow gap and changes direction. The wavefronts are found to bend around the edges as shown below.

Figure 6. Diffraction through a gap

As you can see in th figure 6, if the size of the gap ('aperture') is about the same size as the wavelength, shown by the gap between wavefronts, then semi-circular wavefronts are produced.
However if the gap is much bigger, then the central section passes straight through, with diffraction only occurring at the edges.

A similar effect is seen when wave pass a single edge as shown below. The waves seem to bend around the edge, and this is also a diffraction effect.

Figure 7. Diffraction around an edge.

Note that the waves change direction in the shadow of the barrier. The longer the wavelength, the greater the level of diffraction behind the barrier. (A higher amplitude at large angles). This is why radio waves are relatively unaffected by buildings in cities - they have a very long wavelength and so are diffracted round the buildings, and can be detected behind the building. We don't see this edge effect with visible light waves that have a much smaller wavelength - what little diffraction occurs is at very small angles.

## Ripple Tanks

A ripple tank is a device used to show water waves in a tray. It is actually a very simple and easy to make device. The 'paddle' can be a piece of wood or plastic, suspended on elastic bands. The oscillator is just a motor with a mass added on the end but off-centre, so that as the motor spins it vibrates. The paddle then moves up and down in the water, with the speed controlled by the power supply. A lamp above the water tray means that wavefronts can be seen underneath the tray.

The apparatus can be used to demonstrate reflection, refraction and diffraction, as well as to measure wave speed, wavelength and frequency of the water waves.

Figure 8. A ripple tank for demonstrating wave properties

### Required Practical: Using a ripple tank

#### Describe the use of a ripple tank to show reflection, refraction due to a change in depth, and diffraction through gaps and at edges

The videos below from Debbink Physics YouTube Channel show how the ripple tank can be used to demonstrate changes in direction using barriers in the water.

a). Reflection (See section 3.2a for more diagrams showing reflected waves).

Here, a plastic block has been placed in the water, and water wavefronts can be seen reflecting from the hard 'plane' (straight) surface.

YouTube video - Reflecting Waves in a ripple tank - Debbink Physics.

b). Refraction (See section 3.2b for more diagrams showing refracted wavefronts).

Here, a thin piece of plastic has been placed in the water, making a region of shallow water on the left hand side. This slows the water waves down, and causes the wavefronts to refract at the edge of the shallow region as shown.

YouTube video - Refracting Waves in a ripple tank - Debbink Physics.

c). Diffraction through a gap

Here, notice the semi-circular pattern as shown above in figure 6.

YouTube video - Diffracted Waves in a ripple tank (gap) - Debbink Physics.

d). Diffraction at an edge

In this video, it is harder to spot, but notice the wavefronts bending around the edges a little as shown in figure 7 above.

YouTube video - Diffracted Waves in a ripple tank (edge) - Debbink Physics.

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