What you'll learn
Waves is the unit of AQA GCSE Combined Science: Trilogy that explains how energy is transferred 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 a fixed position and return to it, so the wave carries energy and information but not material. The unit covers the two types of wave, the quantities used to describe them, how to measure wave speed, what happens when waves meet a boundary, and the electromagnetic spectrum with its uses and hazards. By the end you should be able to distinguish transverse from longitudinal waves, define amplitude, wavelength, frequency and period, apply the wave speed equation, describe how to measure the speed of waves in water and in a solid, name the seven groups of the electromagnetic spectrum in order, and give uses and hazards for each. This unit is assessed on Physics Paper 2.
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, producing compressions and rarefactions
Amplitude — the maximum displacement of a point on a wave from its undisturbed position
Wavelength — the distance from a point on one wave to the equivalent point on the adjacent wave, measured in metres
Frequency — the number of waves passing a point each second, measured in hertz
Period — the time taken for one complete wave to pass a point, equal to one divided by the frequency
Wave speed — the speed at which the energy, or the wave, moves through the medium, in metres per second
Refraction — the change in direction of a wave as it crosses a boundary between two media at an angle, caused by a change in its speed
Electromagnetic waves — transverse waves that transfer energy from a source to an absorber and travel at the same speed through a vacuum
Core concepts
Transverse and longitudinal waves
In a transverse wave, the oscillations are perpendicular to the direction of energy transfer. Ripples on the surface of water are the standard example, and all electromagnetic waves are transverse.
In a longitudinal wave, the oscillations are parallel to the direction of energy transfer. The wave travels as a series of compressions, where the particles are pushed together, and rarefactions, where they are spread apart. Sound waves travelling through air are the standard example.
In both cases it is the wave, and therefore the energy, that travels. The particles of the medium simply oscillate about their fixed positions. A floating object on a pond bobs up and down as ripples pass but does not move across the pond, and this observation is worth quoting because it demonstrates the principle directly.
Describing a wave
Amplitude is the maximum displacement of a point from its undisturbed position, measured from the rest position to a peak, not from a peak to a trough. Halving that distance by mistake, or doubling it, is a frequent error.
Wavelength is the distance from any point on one wave to the equivalent point on the next — peak to peak, or trough to trough.
Frequency is the number of complete waves passing a point each second, measured in hertz. A frequency of 50 hertz means 50 waves pass each second.
The period is the time for one complete wave to pass, and it is simply one divided by the frequency. A wave of frequency 25 hertz has a period of 0.04 seconds.
The wave speed 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: 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.
Measuring wave speed
Two methods are required. For waves on the surface of water, a ripple tank is used. The wavelength can be measured by capturing an image of the pattern on a screen and measuring across several waves before dividing, which reduces the percentage uncertainty. The frequency can be found by counting the waves passing a point over a measured time, or from the setting of the vibrating dipper. Multiplying the two gives the speed.
For waves in a solid, waves are sent along a stretched string. The wavelength is found by measuring the length of the visible pattern and the frequency is read from the signal generator driving the vibration. Again, the speed is frequency multiplied by wavelength.
In both practicals, measuring across several wavelengths and dividing is the technique that improves accuracy, and examiners award marks for stating it.
Reflection, transmission and absorption
When a wave arrives at a boundary between two materials, three things can happen: it may be reflected, it may be absorbed by the second material and transfer energy to its store, or it may be transmitted, passing through and continuing.
Which happens depends on the wavelength of the wave and on the properties of the two materials. Often more than one occurs at the same boundary, which is why a window both transmits most light and reflects a little.
Refraction
When a wave crosses a boundary at an angle, it changes direction. This is refraction, and it happens because the wave changes speed as it enters the new medium.
The rule to remember is that a wave slowing down bends towards the normal, and a wave speeding up bends away from the normal. If the wave meets the boundary along the normal, at ninety degrees to the surface, it changes speed but does not change direction.
The frequency of a wave does not change on refraction. Since the speed changes and the frequency does not, the wavelength must change, and this follows directly from the wave speed equation.
The electromagnetic spectrum
Electromagnetic waves are transverse, transfer energy from a source to an absorber, and travel at the same speed through a vacuum or through air. They form a continuous spectrum, grouped into seven regions by wavelength and frequency.
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 part detectable by the human eye, and it occupies a very narrow band of the whole spectrum.
Electromagnetic waves are generated by changes in atoms and in the nuclei of atoms. Gamma rays originate from changes in the nucleus of an atom.
Uses and hazards
Radio waves are used for television and radio broadcasting. Microwaves are used for satellite communications and for cooking food. Infrared is used in electrical heaters, in cooking food and in infrared cameras. Visible light is used in fibre optic communications. Ultraviolet is used in energy-efficient lamps and in sun tanning. X-rays and gamma rays are used in medical imaging and in treatments such as radiotherapy.
The hazards depend on the type of wave and the size of the dose. Ultraviolet waves can cause skin to age prematurely and increase the risk of skin cancer. X-rays and gamma rays are ionising radiation and can cause mutation of genes, which can lead to cancer.
The general pattern is that the higher the frequency, the greater the energy transferred and the greater the potential harm, which is why the hazards cluster at the ultraviolet end of the spectrum.
Worked examples
Example 1: Using the wave speed equation (3 marks)
A sound wave has a frequency of 440 hertz and a wavelength of 0.75 metres. Calculate its speed.
Wave speed equals frequency multiplied by wavelength, which is 440 multiplied by 0.75. This gives 330 metres per second. As a check, this is the accepted approximate speed of sound in air, so the answer is reasonable.
Example 2: Finding wavelength and period (4 marks)
A radio station broadcasts at a frequency of 100 megahertz. Electromagnetic waves travel at 3 times 10 to the power 8 metres per second. Calculate the wavelength and the period.
First convert the frequency: 100 megahertz is 100 million hertz, or 1 times 10 to the power 8 hertz. Wavelength equals speed divided by frequency, which is 3 times 10 to the power 8 divided by 1 times 10 to the power 8, giving 3 metres. The period is one divided by the frequency, which is 1 divided by 1 times 10 to the power 8, giving 1 times 10 to the power minus 8 seconds.
Example 3: Explaining refraction (4 marks)
A ray of light passes from air into glass at an angle to the normal and changes direction. Explain why.
Light travels more slowly in glass than in air. Because the ray meets the boundary at an angle, one side of the wavefront enters the glass and slows down before the other side does. This causes the wavefront to change direction, so the ray bends towards the normal as it enters the denser medium. The frequency is unchanged, so the wavelength decreases as the speed decreases.
Common mistakes and how to avoid them
The most frequent error is measuring amplitude from a peak to a trough. Amplitude is measured from the undisturbed position to a peak, so a peak-to-trough measurement is twice the amplitude.
Students often say that waves transfer matter, or that the water moves along with a ripple. Waves transfer energy; the particles oscillate about fixed positions.
In refraction questions, many answers say the wave bends without explaining that it changes speed. The change in speed is the cause and is where the marks are.
Another regular slip is stating that frequency changes during refraction. Frequency is set by the source and does not change; speed and wavelength both change.
Finally, the electromagnetic spectrum is often listed in the wrong order. Learn it as a sequence from radio waves through to gamma rays, and remember that frequency increases along it while wavelength decreases.
Exam technique for "Physics: Waves"
Convert units before calculating. Frequencies in kilohertz, megahertz and gigahertz, and wavelengths in centimetres or nanometres, appear constantly in this unit and are the main cause of wrong answers.
When using the wave speed equation, write it out, rearrange it if needed, then substitute. Rearranging after substituting numbers is where most algebraic errors occur.
For the required practical, state explicitly that measuring across several wavelengths and dividing reduces the percentage uncertainty. It is a reliable mark.
Where a question asks for a use of a particular electromagnetic wave, give the use and, if asked to justify it, link it to a property. Microwaves are used for satellite communication because they pass through the atmosphere, which is a better answer than naming the use alone.
Quick revision summary
Waves transfer energy without transferring matter. Transverse waves oscillate perpendicular to the direction of energy transfer, longitudinal waves parallel, producing compressions and rarefactions. Amplitude is measured from the undisturbed position to a peak, wavelength from one point to the equivalent point on the next wave, frequency in waves per second, and period is one divided by frequency. Wave speed equals frequency times wavelength, so in a given medium frequency and wavelength are inversely proportional. Speed is measured using a ripple tank for water waves and a stretched string for waves in a solid, measuring several wavelengths to reduce uncertainty. At a boundary a wave may be reflected, absorbed or transmitted, and refraction occurs because the wave changes speed, bending towards the normal when it slows. The electromagnetic spectrum runs from radio waves through microwaves, infrared, visible light, ultraviolet and X-rays to gamma rays, with uses across communication, heating, imaging and treatment, and with ultraviolet, X-rays and gamma rays presenting the greatest hazards.