Properties of waves — AQA GCSE Physics
Test yourself on Properties of waves with AQA GCSE practice questions.
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Properties of waves explained
Four quantities describe any wave. Amplitude is the maximum displacement of a point from its undisturbed position, measured in metres.
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Wavelength, λ, is the distance from one point on a wave to the equivalent point on the next, also in metres. Frequency, f, is the number of complete waves passing a point each second, measured in hertz. Period, T, is the time for one complete wave to pass, in seconds, and the two are reciprocals: T = 1 ÷ f. The speed at which the wave carries energy through the medium links three of them, wave speed = frequency × wavelength, so a 50 Hz ripple of wavelength 0.02 m travels at 1 m/s. Amplitude and frequency are independent, so turning up the volume on a signal generator changes the amplitude while the frequency and wavelength stay the same.
The amplitude of a wave is the maximum displacement of a point on a wave away from its undisturbed position.
Amplitude is measured from the undisturbed, or rest, position of the medium out to a crest, or down to a trough; it is the largest displacement any point reaches. That means the vertical height from a crest to the neighbouring trough is twice the amplitude, a favourite trap in graph questions. On a displacement-distance or displacement-time graph, read the amplitude off the displacement axis from the centre line to the peak, taking care with the scale. Amplitude carries the energy of the wave: a larger amplitude sound wave is louder, and a larger amplitude light wave is brighter, while the frequency of the wave is entirely separate. Amplitude does not depend on frequency or wavelength, so a quiet high-pitched note has both a small amplitude and a short wavelength.
The wavelength of a wave is the distance from a point on one wave to the equivalent point on the adjacent wave.
Wavelength is the distance from any point on a wave to the equivalent point on the next wave: crest to the next crest, trough to the next trough, or compression to the next compression. Measuring one wave alone gives a large percentage uncertainty, so in practice you measure across ten complete waves with a millimetre rule and divide the total by ten. The symbol is λ and the unit is the metre, so a wavelength written in centimetres must be converted before it is used in wave speed = frequency × wavelength. Wavelength and frequency are linked: for a fixed wave speed, a higher frequency always means a shorter wavelength. On a longitudinal wave the equivalent points are two neighbouring compressions, so one definition covers both types of wave.
The frequency of a wave is the number of waves passing a point each second.
Frequency counts complete waves rather than measuring a distance: it is the number of waves passing a fixed point every second, and its unit is the hertz, where 1 Hz is one wave per second. In a ripple tank you count the waves crossing a mark over a measured time and divide, so 40 waves in 10 s gives 4 Hz. Frequency is set by the source, not by the medium, so it is unchanged when a wave crosses a boundary. It is the reciprocal of the period, f = 1 ÷ T, and it appears in wave speed = frequency × wavelength. A higher frequency sound is heard as a higher pitch. Frequencies cover an enormous range: a bass note is around 50 Hz, the upper limit of human hearing about 20 000 Hz, and visible light of the order of 10¹⁴ Hz.
period = f requency T = f period, T, in seconds, s frequency, f, in hertz, Hz The wave speed is the speed at which the energy is transferred (or the wave moves) through the medium.
Period and frequency are reciprocals: T = 1 ÷ f, with the period in seconds and the frequency in hertz. A 50 Hz wave has a period of 1 ÷ 50 = 0.02 s, and a wave with a period of 0.004 s has a frequency of 250 Hz. The period is read from a displacement-time graph as the time for one complete cycle. Wave speed is a different quantity: it is the speed at which the energy, or the wave itself, moves through the medium, measured in m/s, and it is found from wave speed = frequency × wavelength. Sound in air travels at about 330 m/s, while light travels at 3 × 10⁸ m/s. Period and wavelength are easily confused because both are read from a graph: the period comes from a displacement-time graph, the wavelength from a displacement-distance graph.
(Physics only) Students should be able to show how changes in velocity, frequency and wavelength, in transmission of sound waves from one medium to another, are inter-related.
When a sound wave crosses from one medium into another, its frequency does not change, because the frequency is fixed by the source that made it. What changes is the speed, because the speed depends on the medium: sound travels at about 330 m/s in air, roughly 1500 m/s in water and faster still in solids, where the particles are closer together. Since wave speed = frequency × wavelength, holding the frequency fixed forces the wavelength to change in the same ratio as the speed. A 500 Hz note has a wavelength of 330 ÷ 500 = 0.66 m in air, but 1500 ÷ 500 = 3.0 m in water, over four times longer. Pitch is set by frequency, so a note played underwater sounds the same pitch to a diver even though its wavelength there is far longer.
Required practical activity 8: make observations to identify the suitability of apparatus to measure the frequency, wavelength and speed of waves in a ripple tank and waves in a solid and take appropriate measurements.
Required practical 8 measures waves in two places. In a ripple tank, a motorised dipper makes straight ripples whose shadows fall on paper below; freeze them with a stroboscope or a photograph, measure across ten wavelengths with a rule and divide by ten, read the frequency from the motor's signal generator or count ripples passing a mark over 10 s, then use wave speed = frequency × wavelength. For waves in a solid, a vibration generator drives a stretched string until a clear standing pattern forms; the distance between adjacent nodes is half a wavelength, so λ = 2 × that spacing, and the frequency is read from the signal generator. Repeat each measurement and take a mean, and quote the resolution of the rule you used when you report the wavelength.
Your focus
- Label amplitude, wavelength and period on displacement-distance and displacement-time graphs of a wave.
- Calculate the wave speed of a ripple from its measured frequency and wavelength.
- Convert between the frequency and the period of a wave using T = 1 ÷ f.
Show all 21 objectives
- Determine the amplitude of a wave from a displacement-time graph, using the axis scale correctly.
- Calculate the amplitude when only the crest-to-trough distance is given.
- Explain why the amplitude, and not the frequency, decides how loud a sound is.
- Measure a wavelength from a diagram by measuring across ten waves and dividing by ten.
- Calculate a wavelength from a given wave speed and frequency, converting units where needed.
- Explain why the wavelength shortens when the frequency rises at a fixed wave speed.
- Calculate the frequency of a wave from a count of waves passing a point in a measured time.
- Convert a period in seconds into a frequency in hertz, and back again.
- Explain why the frequency of a wave is unchanged when it passes into a different medium.
- Calculate the period of a wave from its frequency, and the frequency from its period.
- Determine the wave speed of a sound wave from its frequency and wavelength.
- Describe what wave speed measures, and distinguish it from the speed of the oscillating particles.
- Calculate the wavelength of a sound of fixed frequency in air and in water from the speeds in each medium.
- Explain why the wavelength must change when a sound wave passes into a medium where it travels faster.
- Identify which of speed, frequency and wavelength stays constant when a wave crosses a boundary.
- Describe a method for finding the speed of water waves in a ripple tank, naming the apparatus used.
- Determine the wavelength of a wave on a vibrating string from the distance between adjacent nodes.
- Explain how measuring across ten waves reduces the percentage uncertainty in the wavelength.
Properties of waves exam tips
Marking Points
- one mark for amplitude as the maximum displacement from the undisturbed position
- one mark for wavelength as the distance between equivalent points on adjacent waves
- one mark for frequency as the number of waves passing a point each second, in hertz
- one mark for period as the time for one wave, with T = 1 ÷ f
- one mark for using wave speed = frequency × wavelength with consistent units
- one mark for amplitude being the maximum displacement of a point on the wave
- one mark for stating that it is measured from the undisturbed or rest position
- one mark for reading the amplitude from a graph using the displacement axis scale
- one mark for halving a crest-to-trough measurement to obtain the amplitude
- one mark for wavelength as the distance from a point on one wave to the equivalent point on the next
- one mark for measuring across several whole waves and dividing by the number of waves
- one mark for a wavelength quoted in metres, after converting from centimetres if needed
- one mark for using λ = wave speed ÷ frequency to calculate a wavelength
- one mark for frequency as the number of complete waves passing a point each second
- one mark for the unit hertz, Hz
- one mark for counting waves over a measured time and dividing by that time
- one mark for using f = 1 ÷ T to convert a period into a frequency
- one mark for writing period = 1 ÷ frequency
- one mark for a correct substitution, such as T = 1 ÷ 50
- one mark for the period given in seconds
- one mark for describing wave speed as the speed at which energy, or the wave, moves through the medium
- one mark for using wave speed = frequency × wavelength
- one mark for stating that the frequency stays the same when the sound crosses the boundary
- one mark for stating that the speed changes because the medium has changed
- one mark for using wave speed = frequency × wavelength to link the change of speed to the change of wavelength
- one mark for a correct calculation of the new wavelength, with the unit m
- one mark for measuring across ten wavelengths and dividing by ten
- one mark for using a stroboscope or a photograph to freeze the ripple pattern before measuring
- one mark for reading the frequency from the signal generator, or counting waves passing a point in a measured time
- one mark for stating that the wavelength on the string is twice the distance between adjacent nodes
- one mark for calculating the speed using wave speed = frequency × wavelength
Examiner Tips
- 💡Check the axis of a wave graph: a displacement-distance graph shows wavelength, a displacement-time graph shows period.
- 💡Convert every length to metres before using wave speed = frequency × wavelength.
- 💡Label amplitude with an arrow that starts on the centre line, not at a trough.
- 💡Draw the undisturbed line on the diagram first, then measure from it.
- 💡Read the graph scale before you measure; each small square is rarely worth one unit.
- 💡If asked for the amplitude from a crest-to-trough value, show the division by two in your working.
- 💡When labelling wavelength on a diagram, draw the arrow between two identical points, crest to crest.
- 💡Write the division by ten explicitly when you measure several waves together.
- 💡State the unit at every stage so a conversion error shows up before the final answer.
- 💡Count waves over ten seconds rather than one, then divide; it reduces the timing uncertainty.
- 💡Write 1 ÷ T rather than T when converting; the reciprocal step is where marks are lost.
- 💡Give the unit Hz with every frequency answer, including ones read from a graph.
- 💡Write the reciprocal as a fraction on the page; it makes an inverted substitution obvious.
- 💡Check the size of your answer: a period of many seconds implies a frequency well below 1 Hz.
- 💡State which medium a speed applies to; wave speed changes from one medium to another.
- 💡Start these answers with 'the frequency is unchanged'; everything else follows from it.
- 💡Set the two situations out side by side, each with its own speed and wavelength.
- 💡State the ratio as well as the numbers, such as 'the speed is about 4.5 times greater, so the wavelength is too'.
- 💡Name the apparatus precisely: ripple tank, dipper, signal generator, stroboscope, metre rule.
- 💡Say how you reduce uncertainty, by measuring many waves or many oscillations, not by 'being careful'.
- 💡Quote the equation you will use before describing the measurements, so the plan reads purposefully.
Common Mistakes
- measuring the amplitude from a crest down to a trough instead of from the undisturbed position
- giving frequency the unit s or m rather than Hz
- confusing the period with the wavelength because both are read off a graph
- writing wave speed = frequency ÷ wavelength
- quoting the full crest-to-trough height as the amplitude
- measuring the amplitude along the time or distance axis instead of the displacement axis
- saying amplitude is the height of the wave without saying what it is measured from
- assuming a larger amplitude also means a higher frequency
- measuring from a crest to the next trough, which is only half a wavelength
- measuring a single wave on a small diagram rather than ten waves to reduce uncertainty
- leaving a wavelength in centimetres inside a calculation whose answer is wanted in m/s
- confusing wavelength with amplitude when labelling a diagram
- counting the waves in 10 s and quoting the count itself as the frequency
- confusing frequency with wave speed, so a higher frequency is taken to mean a faster wave
- giving frequency the unit seconds because it involves time
- assuming frequency changes when a wave moves into a new medium
- reading the printed formula as T = f and multiplying rather than taking the reciprocal
- quoting a period in hertz or a frequency in seconds
- using the speed of light in a calculation about a sound wave
- dividing frequency by wavelength instead of multiplying when finding the wave speed
- saying the frequency changes at the boundary and the wavelength stays the same
- claiming sound slows down when it passes from air into water
- pairing the speed in one medium with the wavelength in the other inside the same substitution
- assuming the pitch of the note changes when it enters a new medium
- measuring a single ripple, so the percentage uncertainty in the wavelength is large
- taking the node-to-node spacing on a vibrating string as a whole wavelength
- counting waves for one second by eye instead of counting over ten seconds and dividing
- forgetting to convert the measured wavelength from centimetres to metres before finding the speed