What you'll learn
Waves and their properties is the topic in CXC CSEC Physics that explains how energy travels from one place to another without any matter travelling with it. That single idea is the key to the whole unit: when a wave passes, the particles of the medium oscillate about fixed positions and return to them, so the wave carries energy and information but not material. The topic covers the two types of wave, the quantities used to describe them, the wave equation, the four behaviours waves exhibit at boundaries and obstacles, and the electromagnetic spectrum. By the end of this guide you should be able to distinguish transverse from longitudinal waves, define and use amplitude, wavelength, frequency and period, apply the wave equation, explain reflection, refraction, diffraction and interference, and state the order, uses and hazards of the electromagnetic spectrum.
Key terms and definitions
Wave — a disturbance that transfers energy from one place to another without transferring matter
Transverse wave — a wave in which the oscillations are perpendicular to the direction of energy transfer
Longitudinal wave — a wave in which the oscillations are parallel to the direction of energy transfer
Compression — a region of a longitudinal wave where particles are pushed close together
Rarefaction — a region of a longitudinal wave where particles are spread apart
Amplitude — the maximum displacement of a point from its undisturbed position
Wavelength — the distance between two consecutive points in phase, measured in metres
Frequency — the number of complete waves passing a point each second, measured in hertz
Period — the time for one complete wave to pass a point, equal to one divided by the frequency
Wavefront — a line joining points on a wave that are in phase, such as a line of crests
Refraction — the change in direction of a wave crossing a boundary at an angle, caused by a change in speed
Diffraction — the spreading of a wave as it passes through a gap or around an obstacle
Interference — the combination of two waves meeting at a point, producing reinforcement or cancellation
Core concepts
Transverse and longitudinal waves
In a transverse wave, the oscillations are perpendicular to the direction in which the energy travels. Water ripples, waves on a rope and all electromagnetic waves are transverse. Transverse waves have crests and troughs.
In a longitudinal wave, the oscillations are parallel to the direction of energy transfer. The wave travels as a series of compressions, where particles are pushed together, and rarefactions, where they are spread apart. Sound is the standard example, and a slinky spring pushed back and forth demonstrates it well.
In both cases it is the wave, and therefore the energy, that travels. The particles of the medium oscillate about fixed positions. A cork floating on a pond bobs up and down as ripples pass but does not travel across the pond — an observation worth quoting because it demonstrates the principle directly.
A key distinction: longitudinal waves require a material medium and cannot travel through a vacuum, which is why sound cannot be heard in space. Electromagnetic waves, being transverse, need no medium.
Describing a wave
Amplitude is the maximum displacement of a point from its undisturbed position, measured from the rest position to a crest, not from crest to trough. The amplitude determines the energy carried by the wave: a larger amplitude means more energy, which for sound means louder and for light means brighter.
Wavelength is the distance between two consecutive points in phase — crest to crest, or trough to trough, or compression to compression.
Frequency is the number of complete waves passing a point each second, measured in hertz. It is determined by the source and does not change when the wave moves into a different medium.
The period is the time for one complete wave to pass, and it is the reciprocal of the frequency. A wave of frequency 50 hertz has a period of 0.02 seconds.
A wavefront is a line joining points in phase, and wavefront diagrams are used to represent reflection, refraction and diffraction.
The wave equation
Wave speed equals frequency multiplied by wavelength, with speed in metres per second, frequency in hertz and wavelength in metres.
It rearranges to give frequency equals speed divided by wavelength, and wavelength equals speed divided by frequency.
An important consequence follows: in a given medium the wave speed is fixed, so frequency and wavelength are inversely proportional. A higher frequency means a shorter wavelength. This is why gamma rays, at the high-frequency end of the electromagnetic spectrum, have the shortest wavelengths.
Unit conversion is the main source of error. Frequencies given in kilohertz, megahertz or gigahertz, and wavelengths in centimetres or nanometres, must be converted before substituting.
Reflection
When a wave meets a barrier it may be reflected. The angle of incidence equals the angle of reflection, both measured from the normal, which is the line perpendicular to the surface at the point of incidence.
Reflection does not change the wave's speed, frequency or wavelength; only its direction changes.
Echoes are reflections of sound, and the same principle underlies radar and ultrasound imaging.
Refraction
When a wave crosses a boundary between two media at an angle, it changes direction. This is refraction, and it occurs because the wave changes speed in the new medium.
The rule is that a wave slowing down bends towards the normal, and a wave speeding up bends away from the normal. A wave meeting the boundary along the normal, at ninety degrees to the surface, changes speed but not direction.
In water waves, the speed decreases as the water becomes shallower, so waves refract towards the normal when moving from deep to shallow water. This is why waves turn to become more nearly parallel to a beach as they approach it.
Critically, the frequency does not change during refraction, because it is set by the source. Since the speed changes and the frequency does not, the wavelength must change — and this follows directly from the wave equation.
Diffraction
Diffraction is the spreading of waves as they pass through a gap or around the edge of an obstacle.
The amount of diffraction depends on the relationship between the wavelength and the size of the gap. Diffraction is greatest when the gap width is comparable to the wavelength. A gap much wider than the wavelength produces only slight spreading at the edges, while a gap of about one wavelength produces waves spreading out in almost a semicircle.
This explains a familiar observation: sound diffracts around a doorway and can be heard around a corner, because its wavelength is comparable to the width of the door, whereas light has a far shorter wavelength and does not noticeably diffract, so you cannot see around the corner.
Diffraction does not change the wavelength, frequency or speed of the wave — only the shape of the wavefronts.
Interference
When two waves meet at a point, their displacements add. This is interference.
Constructive interference occurs where the two waves arrive in phase, so a crest meets a crest. The displacements add, producing a larger amplitude — a louder sound or a brighter light.
Destructive interference occurs where they arrive out of phase, so a crest meets a trough. The displacements cancel, producing a smaller amplitude or none at all.
For a stable interference pattern the two sources must be coherent, meaning they have the same frequency and a constant phase relationship.
The electromagnetic spectrum
Electromagnetic waves are transverse, transfer energy from a source to an absorber, require no medium, and travel through a vacuum at the same speed of about 3 times 10 to the power 8 metres per second.
In order of increasing frequency and decreasing wavelength, the groups are radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. Visible light is the only region detectable by the human eye and occupies a very narrow band.
The uses are examinable. Radio waves are used for radio and television broadcasting. Microwaves are used for satellite communication, mobile phones and cooking. Infrared is used in heaters, remote controls and thermal imaging. Visible light is used for seeing, photography and fibre optic communication. Ultraviolet is used in security marking, sterilising equipment and sun lamps. X-rays are used for medical imaging and inspecting welds. Gamma rays are used to sterilise equipment and food and to treat cancer.
The hazards increase with frequency. Microwaves can cause internal heating of body tissue. Infrared causes skin burns. Ultraviolet damages surface cells, causes premature ageing of the skin and increases the risk of skin cancer, and can damage the eyes. X-rays and gamma rays are ionising and can cause mutation of cells, leading to cancer.
Worked examples
Example 1: Using the wave equation (3 marks)
A wave has a frequency of 250 hertz and a wavelength of 1.4 metres. Calculate its speed.
Wave speed equals frequency multiplied by wavelength.
Substituting gives 250 × 1.4 = 350 metres per second.
The unit follows from hertz multiplied by metres, which gives metres per second.
Example 2: Converting units before calculating (4 marks)
A radio station broadcasts at 92.5 megahertz. Electromagnetic waves travel at 3.0 times 10 to the power 8 metres per second. Calculate the wavelength.
First convert the frequency. One megahertz is 1 × 10 to the power 6 hertz, so 92.5 megahertz is 9.25 × 10 to the power 7 hertz.
Wavelength equals speed divided by frequency, which is 3.0 × 10 to the power 8 divided by 9.25 × 10 to the power 7.
This gives 3.24 metres to three significant figures. A radio wavelength of a few metres is reasonable, which confirms the conversion was done correctly.
Example 3: Explaining refraction (4 marks)
Water waves travel from a deep region into a shallow region, meeting the boundary at an angle. Describe and explain what happens to the waves.
The waves slow down as they enter the shallow water, because wave speed in water decreases with depth.
Because the waves meet the boundary at an angle, one part of each wavefront enters the shallow water and slows before the rest does. This causes the wavefronts to change direction, and the waves bend towards the normal.
The frequency is unchanged, since it is determined by the source. As the speed has decreased and the frequency is constant, the wave equation requires that the wavelength also decreases, so the wavefronts appear closer together in the shallow region.
Common mistakes and how to avoid them
The most frequent error is measuring amplitude from crest to trough. Amplitude is measured from the undisturbed position to a crest, so a crest-to-trough measurement is twice the amplitude.
Students often say that waves transfer matter, or that the water moves forward with a ripple. Waves transfer energy; the particles oscillate about fixed positions.
In refraction questions, many answers state that the wave bends without explaining that it changes speed. The change in speed is the cause and carries the marks.
Another frequent slip is claiming that frequency changes during refraction. Frequency is set by the source; speed and wavelength change.
Many candidates confuse diffraction with refraction. Diffraction is spreading through a gap or around an obstacle; refraction is bending at a boundary due to a speed change.
Finally, the electromagnetic spectrum is often listed out of order. Learn it as a sequence from radio waves to gamma rays, with frequency increasing and wavelength decreasing along it.
Exam technique for "Waves and Their Properties"
Convert all units before substituting into the wave equation. Frequencies in kilohertz, megahertz and gigahertz and wavelengths in centimetres or nanometres appear constantly.
Write the equation, rearrange it if needed, then substitute. Rearranging after substituting numbers is where most algebraic errors occur.
When asked to explain any wave behaviour, name the property that changes and the property that does not. For refraction, speed and wavelength change while frequency does not; for diffraction, nothing changes but the shape of the wavefronts.
For questions on the electromagnetic spectrum, give the use and, where asked to justify it, link it to a property of that region. Microwaves are used for satellite communication because they pass through the atmosphere.
When drawing wavefront diagrams, show the change in spacing as well as direction. Refraction into a slower medium gives wavefronts that are both bent and closer together.
Quick revision summary
Waves transfer energy without transferring matter, with particles oscillating about fixed positions. Transverse waves oscillate perpendicular to the direction of travel and include water ripples and all electromagnetic waves; longitudinal waves oscillate parallel and travel as compressions and rarefactions, as sound does, and require a medium. Amplitude is measured from the undisturbed position to a crest and determines energy; wavelength is the distance between consecutive points in phase; frequency is waves per second, set by the source; and period is one divided by frequency. Wave speed equals frequency multiplied by wavelength, so in a given medium frequency and wavelength are inversely proportional. Reflection obeys the equal angles rule about the normal. Refraction occurs because the wave changes speed, bending towards the normal when slowing, with frequency unchanged and wavelength therefore changing. Diffraction is spreading through a gap, greatest when the gap is comparable to the wavelength, which is why sound bends around a doorway but light does not. Interference is constructive in phase and destructive out of phase, requiring coherent sources. The electromagnetic spectrum runs from radio waves through microwaves, infrared, visible light, ultraviolet and X-rays to gamma rays, all travelling at the same speed in a vacuum, with hazards increasing at the high-frequency end.