IGCSE Co-ordinated Sciences · Area 3 · Physics

Waves

Waves covers how energy travels without matter travelling: wave properties, the reflection and refraction of light, thin lenses, the electromagnetic spectrum and sound.

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Syllabus coverage

  • Know that waves transfer energy without transferring matter
  • Describe what is meant by wave motion as illustrated by vibrations in ropes and springs, and by experiments using water waves
  • Describe the features of a wave in terms of wavefront, wavelength, frequency, crest (peak), trough, amplitude and wave speed
  • Recall and use the equation for wave speed, v = f x wavelength
  • Know that for a transverse wave, the direction of vibration is at right angles to the direction of propagation, and understand that electromagnetic radiation, water waves and seismic S-waves (secondary) can be modelled as transverse
  • Know that for a longitudinal wave, the direction of vibration is parallel to the direction of propagation, and understand that sound waves and seismic P-waves (primary) can be modelled as longitudinal
  • Describe how waves can undergo reflection at a plane surface, refraction due to a change of speed, and diffraction through a narrow gap
  • Describe the use of a ripple tank to show reflection at a plane surface, refraction due to a change in speed caused by a change in depth, diffraction due to a gap, and diffraction due to an edge
  • Describe how wavelength and gap size affect diffraction through a gap
  • Describe how wavelength affects diffraction at an edge
  • Define and use the terms normal, angle of incidence and angle of reflection; state that for reflection the angle of incidence is equal to the angle of reflection, and recall and use this relationship
  • Describe the formation of an optical image by a plane mirror and give its characteristics, that is the same size, the same distance from the mirror and virtual; use simple constructions, measurements and calculations for reflection by plane mirrors
  • Define and use the terms normal, angle of incidence and angle of refraction, and describe an experiment to show refraction of light by transparent blocks of different shapes
  • Describe the passage of light through a transparent material, limited to the boundaries between two mediums only; state the meaning of critical angle, and describe internal reflection and total internal reflection using both experimental and everyday examples
  • Define refractive index, n, as the ratio of the speeds of a wave in two different regions, and recall and use the equations n = sin i / sin r and n = 1 / sin c

Part of the IGCSE Co-ordinated Sciences syllabus 0654 / 0973.

The anatomy of a waveAmplitude is how far a particle moves from its rest position. Wavelength is the distance between two adjacent pointsin phase.A transverse wave: the particles vibrate at right angles to the direction of travelamplitudewavelengthcresttroughrest positiondirection of travelA longitudinal wave: the particles vibrate along the direction of travelcompressionrarefactioncompressionwavelength (compression to compression)Amplitude relates to the energy of the wave; frequency relates to its pitch in sound, or to its colour in light.
The anatomy of a wave: crests and troughs, the wavelength measured between successive crests, the amplitude measured from the rest position to a crest, and the wavefronts drawn at right angles to the direction in which the wave travels.

General Properties of Waves

Waves transfer energy from place to place without transferring matter. This topic covers the features of a wave, the difference between transverse and longitudinal waves, the wave equation v = f x wavelength, and how waves reflect, refract and diffract.

The anatomy of a waveAmplitude is how far a particle moves from its rest position. Wavelength is the distance between two adjacent pointsin phase.A transverse wave: the particles vibrate at right angles to the direction of travelamplitudewavelengthcresttroughrest positiondirection of travelA longitudinal wave: the particles vibrate along the direction of travelcompressionrarefactioncompressionwavelength (compression to compression)Amplitude relates to the energy of the wave; frequency relates to its pitch in sound, or to its colour in light.

Light

Light is reflected, refracted, focused and dispersed as it travels through different materials. This topic covers the law of reflection and the image formed by a plane mirror, refraction and refractive index, critical angle and total internal reflection including optical fibres, thin converging and diverging lenses with ray diagrams, and the dispersion of white light by a prism.

The Electromagnetic Spectrum

The electromagnetic spectrum is the family of waves from radio waves to gamma rays. They all travel at the same speed in a vacuum but differ in wavelength and frequency, which decides what each region is used for and how it can harm the body. This topic covers the order of the spectrum, the uses and dangers of each region, satellite communication, and digital and analogue signals.

Sound

Sound is a longitudinal wave of compressions and rarefactions produced by a vibrating source and carried through a medium. This topic covers how fast sound travels in solids, liquids and gases, what amplitude and frequency do to loudness and pitch, and how echoes and ultrasound are used in sonar, medical scanning and non-destructive testing.

Key terms you must be able to define

Wave
A disturbance that transfers energy from one place to another without transferring matter.
Transverse wave
A wave in which the direction of vibration is at right angles to the direction of propagation, for example light, a water surface wave or a seismic S-wave.
Longitudinal wave
A wave in which the direction of vibration is parallel to the direction of propagation, for example a sound wave or a seismic P-wave.
Wavelength
The distance between two successive crests, or between any two successive points on a wave that are in step; measured in metres (m).
Amplitude
The maximum displacement of a point from its rest position, measured from the middle line of the wave to a crest; measured in metres (m).
Frequency
The number of complete waves passing a point each second; measured in hertz (Hz), where 1 Hz = one wave per second.
Period
The time taken for one complete wave to pass a point; measured in seconds (s), and equal to 1 / frequency.
Diffraction
The spreading of a wave as it passes through a gap or around the edge of an obstacle; greatest when the gap is similar to or smaller than the wavelength.
Normal
The line drawn perpendicular to a surface at the point where a ray of light meets it. All angles of incidence, reflection and refraction are measured from the normal.
Refractive index, n
The ratio of the speed of light in a vacuum to the speed of light in the material, n = speed in a vacuum / speed in the material. It has no unit. It can also be found from n = sin i / sin r.
Critical angle, c
The angle of incidence in the denser medium at which the angle of refraction is exactly 90 degrees, so the refracted ray runs along the boundary. It is given by sin c = 1 / n.
Total internal reflection
The complete reflection of light back into a denser medium when it meets a boundary with a less dense medium at an angle of incidence greater than the critical angle. It is the principle behind optical fibres.

Applied to the real world

Cambridge sets Co-ordinated Sciences in unfamiliar contexts - a hospital, a power station, a farm, a laboratory. Use these as models for how to apply the science, then write your own.

At sea

A tsunami is a water wave produced by an earthquake on the sea bed. It can carry enough energy to flood a coastline thousands of kilometres away, yet the water itself only moves up and down as the wave passes, because a wave transfers energy and not matter. Tsunamis have extremely long wavelengths, so they diffract very little and keep their energy concentrated in a narrow beam as they cross the ocean.

In a hospital

An ultrasound scanner sends longitudinal sound waves into the body. When the waves cross from one type of tissue into another their speed changes, so they are partly reflected and partly refracted at each boundary. The reflected pulses are timed and turned into a picture of the inside of the body without any need for surgery.

In a communications network

Radio and microwave signals are transverse electromagnetic waves. Their frequency is fixed by the transmitter, so when a signal passes from the air into a cable its speed and wavelength change but its frequency does not. Satellite dishes are lined up using the reflection rule that the angle of incidence equals the angle of reflection for the incoming waves.

In a harbour

Sea waves diffract as they pass through the narrow entrance to a harbour, spreading out and losing their direction. Engineers design breakwaters so that long-wavelength swell diffracts around the ends of the wall and carries less energy into the sheltered water, which keeps moored boats calm.

In a seismology station

Earthquakes produce P-waves, which are longitudinal, and S-waves, which are transverse. The two travel at different speeds and refract as they pass through the different layers of the Earth. By timing their arrival at stations around the world, scientists work out the structure of the Earth's interior, including its liquid outer core.

In a bathroom

A plane mirror gives a virtual image that is the same size as your face and the same distance behind the mirror as you are in front of it. If you stand 0.6 m from the mirror, your image is 0.6 m behind it, so you and your image are 1.2 m apart. This is why you have to move twice as far as you expect to change the apparent distance in the mirror.

Flashcards

Click a card to flip it. Mark honestly — the tracker uses this.

Q1What does a wave transfer from place to place?
Energy, and it does so without transferring matter.
Q2In a transverse wave, what is the direction of vibration?
At right angles (perpendicular) to the direction of propagation.
Q3In a longitudinal wave, what is the direction of vibration?
Parallel to the direction of propagation.
Q4Give two examples of transverse waves.
Electromagnetic radiation such as light, and water surface waves (seismic S-waves are also transverse).
Q5Give two examples of longitudinal waves.
Sound waves and seismic P-waves (ultrasound is also longitudinal).
Q6Define the wavelength of a wave and give its unit.
The distance between two successive crests, or any two successive points in step; measured in metres (m).
Q7Define frequency and give its unit.
The number of complete waves passing a point each second; measured in hertz (Hz).
Q8Define the amplitude of a wave.
The maximum displacement of a point from its rest position, measured in metres (m).
Q9Write the wave equation.
v = f x wavelength, where v is wave speed in m/s, f is frequency in Hz and wavelength is in m.
Q10How is the period of a wave related to its frequency?
Period = 1 / frequency. The period is the time for one complete wave and is measured in seconds.
0 of 10 marked as known

Exam-style questions

9 questions, 28 marks. Write your answer, then reveal the mark scheme and tick each point you actually made. Answering honestly here is what makes the rest of the site useful.

StateAO11 mark
State what is transferred from one place to another by a wave.

Mark scheme — tick each point you actually made

Examiner tip: One word is enough, but add 'without transferring matter' if the question has room, because it shows you understand the key idea.
StateAO12 marks
State the direction of vibration of a transverse wave relative to the direction of propagation, and give one example of a transverse wave.

Mark scheme — tick each point you actually made

Examiner tip: 'At right angles' is the phrase that scores. For the example, do not give sound or a P-wave, because those are longitudinal.
DefineAO12 marks
Define the wavelength of a wave and state its unit.

Mark scheme — tick each point you actually made

Examiner tip: A definition that says 'the length of a wave' is too vague. Name two points that are in step, such as two successive crests.
CalculateAO23 marks
A water wave in a ripple tank has a frequency of 12 Hz and a wavelength of 0.25 m. Calculate the speed of the wave. Give the unit with your answer.

Mark scheme — tick each point you actually made

Examiner tip: Write the equation, then the substitution, then the answer with its unit. The unit carries a mark, and the frequency and wavelength are already in hertz and metres.
CalculateAO23 marks
A sound wave of frequency 660 Hz travels through air at a speed of 330 m/s. Calculate the wavelength of the sound wave. Give the unit with your answer.

Mark scheme — tick each point you actually made

Examiner tip: Rearrange the wave equation before you substitute. The wavelength comes out in metres because the speed is in m/s and the frequency is in Hz.
DescribeAO23 marks
Describe how a ripple tank can be used to show the refraction of water waves.

Mark scheme — tick each point you actually made

Examiner tip: Name the change in depth as the cause, then the change in speed, then the change in direction. All three links are needed for the marks.
ExplainAO24 marks
Explain how the amount of diffraction of a water wave passing through a gap depends on the width of the gap and on the wavelength of the wave.

Mark scheme — tick each point you actually made

Examiner tip: Compare the gap with the wavelength in both directions: gap close to the wavelength gives most spreading, a much wider gap gives least. Mention the effect of wavelength as well as gap size.
CompareAO24 marks
Compare a transverse wave with a longitudinal wave, referring to the direction of vibration, the features of each wave and one example of each.

Mark scheme — tick each point you actually made

Examiner tip: A comparison needs both sides. Give the direction of vibration for each type, not just for one, and name one example of each.
PlanAO36 marks
A student wants to use a ripple tank to investigate how the diffraction of water waves depends on the width of the gap the waves pass through. Plan the experiment, including how the pattern is observed and how a fair comparison is made.

Mark scheme — tick each point you actually made

Examiner tip: A good plan fixes everything except the variable being tested. Keep the depth and the frequency constant, change only the gap width, and say how you will measure the spreading.

Exam technique for this topic

  • State the direction of vibration relative to the direction of propagation. For a transverse wave write 'at right angles' and for a longitudinal wave write 'parallel'; vague words such as 'sideways' do not score.
  • When a wave is refracted, the frequency does not change. Only the speed and the wavelength change, because the frequency is fixed by the source.
  • In v = f x wavelength, convert every quantity to metres, metres per second and hertz before substituting. A wavelength given in centimetres or a frequency given in kilohertz must be converted first.
  • Amplitude is measured from the rest position to a crest, which is half the crest-to-trough distance. Do not write the full crest-to-trough height as the amplitude.
  • For reflection, always measure the angle of incidence and the angle of reflection from the normal, never from the surface itself.

Why students lose marks here

A student wroteA student wrote: 'When a wave refracts, its frequency changes.'
Why it loses marksThe frequency of a wave is set by its source and cannot change when the wave enters a new medium. What changes is the speed, and with it the wavelength. Saying the frequency changes is the commonest error in refraction questions.
The answer that scoresWhen a wave crosses into a new medium its speed changes, so the wave bends. Because v = f x wavelength and the frequency is fixed by the source, the wavelength must change by the same factor as the speed. If the wave slows down the wavelength becomes shorter, but the frequency stays the same.
A student wroteA student wrote: 'The amplitude of a wave is the distance from a crest to the next trough.'
Why it loses marksCrest to trough is twice the amplitude. The amplitude is measured from the rest position to a crest, so this answer gives double the correct value and loses the mark.
The answer that scoresThe amplitude is the maximum displacement of a point from its rest position, measured from the middle line of the wave up to a crest or down to a trough. The distance from a crest to the next trough is twice the amplitude, not the amplitude itself.
A student wroteA student wrote: 'Waves carry matter along with them.'
Why it loses marksA wave transfers energy, not matter. The particles of the medium vibrate about fixed positions and return to where they started, so nothing is carried forward except energy.
The answer that scoresA wave transfers energy from one place to another without transferring matter. In a water wave the water particles move up and down and end where they began, so it is the energy of the wave that travels forward. A floating ball bobs up and down as a wave passes but is not carried along with it.
A tsunami crossing the ocean: the enormous energy of the wave travels thousands of kilometres, while the water particles themselves only move up and down as the wave passes.
A student wroteA student wrote: 'Making the gap wider makes the waves diffract more.'
Why it loses marksThis is the wrong way round. Diffraction is greatest when the gap is about the same size as the wavelength; as the gap gets wider the waves spread less and less.
The answer that scoresDiffraction is the spreading of waves as they pass through a gap. The spreading is greatest when the width of the gap is similar to or smaller than the wavelength. If the gap is much wider than the wavelength the waves pass through with very little spreading, so widening the gap reduces diffraction.

Where this fits in IGCSE Co-ordinated Sciences

This page is one topic of Cambridge IGCSE Co-ordinated Sciences 0654 / 0973. IGCSE Co-ordinated Sciences is the course home: every area and every topic in Cambridge's own order, the papers you sit and what each one tests, and the exam-practice tools. The full topic list, with each topic linked to its revision page, is on the IGCSE Co-ordinated Sciences syllabus page.