AQA GCSE Combined Science Foundation (8464), Foundation tier · Physics › Waves › Waves in air, fluids and solids
Practise Properties of waves. 9 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
The quantities used to describe a wave (amplitude, wavelength, frequency, period and wave speed) and the wave equation v = f λ. Expect calculations, reading values from wave diagrams, and questions on the waves required practical, where you measure waves in a ripple tank and on a stretched string.
Key facts
Amplitude = maximum displacement from the undisturbed position
Wavelength = distance from a point on one wave to the equivalent point on the next wave
Frequency = number of waves passing a point each second (Hz)
Period: T = 1 ÷ f (T in s, f in Hz)
Wave speed = speed at which energy is transferred through the medium
wave speed = frequency × wavelength: v = f λ (learn it)
v in m/s, f in Hz, λ in m
1 kHz = 103 Hz; 1 MHz = 106 Hz; 1 cm = 0.01 m
Notes
Describing a wave
diagram
Amplitude: the maximum displacement of a point on a wave away from its undisturbed (rest) position. Measure from the middle line to a crest, not from crest to trough.
Wavelength (λ): the distance from a point on one wave to the equivalent point on the next wave, e.g. crest to crest, or from the middle of one compression to the middle of the next.
Amplitude: rest position to crest. Wavelength: one crest to the next.
Frequency (f): the number of waves passing a point each second, in hertz (Hz). 1 Hz = 1 wave per second.
Period (T): the time for one complete wave to pass a point, in seconds. T = 1 ÷ f.
Wave speed (v): the speed at which energy is transferred (or the wave moves) through the medium, in m/s.
The wave equation
wave speed = frequency × wavelength, v = f λ. You must remember this equation.
Units: v in m/s, f in Hz, λ in m. Convert first: 1 kHz = 1000 Hz, 1 MHz = 1 000 000 Hz, 1 cm = 0.01 m, 1 mm = 0.001 m.
Rearranged: f = v ÷ λ and λ = v ÷ f.
If the speed stays the same, doubling the frequency halves the wavelength.
Measuring wave speed (required practical)
diagram
Speed of sound in air: two people stand a measured distance apart (at least 100 m). One makes a sound that can also be seen, such as banging two blocks together; the other starts a stopwatch on seeing it and stops it on hearing it. Speed = distance ÷ time. The long distance makes reaction time matter less; repeat and find a mean.
Ripple tank: a lamp above the tank shows the waves as bright and dark lines on paper below. Measure the length of, say, 10 waves with a ruler and divide by 10 to get λ. Count the waves passing a point in 10 s and divide by 10 to get f. Then v = f λ. A photo with a ruler in view makes measuring easier.
Ripple tank: measure λ and count waves on the paper below.
Waves on a string: a vibration generator shakes a string stretched over a pulley by hanging masses. Adjust the frequency on the signal generator until a steady wave pattern appears. Each loop is half a wavelength, so measure across as many loops as possible. Read f from the signal generator, then v = f λ.
How to answer each type of question
Read the amplitude or wavelength from a diagram or graph
1 to 2 marksGrade 3
Amplitude: measure from the middle (rest) line to the top of a crest.
Wavelength: measure one complete cycle, e.g. from one crest to the next.
Check the scale on each axis and give the unit.
Example. The graph shows the displacement of the water at different distances along a water wave at one instant.
(a) Give the amplitude of the wave. (b) Give the wavelength of the wave.
Show the model answerHide the model answer
(a) 3 cm (1) (b) From one crest to the next: 50 − 10 = 40 cm (1)
Calculate wave speed, frequency or wavelength
2 to 3 marksGrade 5
Write down v = f λ.
Convert to Hz and m.
Substitute, rearranging if needed (f = v ÷ λ, λ = v ÷ f).
Give the answer with its unit.
Example. A sound wave in air has a frequency of 1.7 kHz. The speed of sound in air is 340 m/s. Calculate the wavelength of the sound wave.
Show the model answerHide the model answer
1.7 kHz = 1700 Hz (1) λ = v ÷ f = 340 ÷ 1700 (1) λ = 0.20 m (1)
Don’t lose marks
Measuring the amplitude from crest to trough, which gives twice the amplitude.
Forgetting to convert kHz to Hz, or cm to m, before using v = f λ.
Counting crests instead of gaps when finding the wavelength from several waves.
Saying frequency is 'how fast the wave travels'. Frequency is waves per second; speed is distance per second.
In method questions, not saying how the measurements are made more accurate (measure many waves and divide, repeat and find a mean).
More tips
Memory tricks
Formula triangle: v on top, f and λ underneath. Cover the quantity you want.
Count the gaps, not the crests: from the 1st to the 6th crest is 5 wavelengths.
T and f are opposites: T = 1 ÷ f and f = 1 ÷ T. Remember 1 ms = 0.001 s.
Calculator: enter 1.7 kHz as 1.7 × 103 using the ×10x key, so you never miss a zero.
Sense check: sound in air travels at about 340 m/s, while ripples in a ripple tank travel at tens of centimetres per second.
Exam technique
Show the equation, the substitution and the answer with its unit: each is often a separate mark.
Give answers to a sensible number of significant figures, usually the same as the data (often 2 or 3).
In practical questions, name the equipment and say what you measure with it. A photograph or a stroboscope 'freezes' the ripples so they are easier to measure.
If a question gives the time for one wave, that is the period: use f = 1 ÷ T to get the frequency.
What each grade needs
What you need to be able to do, from the first marks up to the top grade.
Grade 3
Label amplitude and wavelength on a diagramAmplitude: from the undisturbed position to a crest (or trough). Wavelength: one complete wave, e.g. crest to crest.
Grade 4
Define frequency and periodFrequency is the number of waves passing a point each second (Hz); the period is the time for one wave (s).
Grade 4
Calculate wave speed using v = f λMultiply the frequency in Hz by the wavelength in m to get the wave speed in m/s.
Grade 5
Use T = 1/fFind the period from the frequency, or the frequency from the period, e.g. f = 50 Hz gives T = 1 ÷ 50 = 0.02 s.
Required practical:Waves (method, variables and exam tips)
Quick recall
Cover the answers and test yourself. The app has these as flashcards that come back just before you'd forget them.
The student measures the distance from the first bright line to the eleventh bright line. The distance is 27 cm. Calculate the wavelength of the waves.
2.7 cm
Write down the equation that links wave speed, frequency and wavelength.
wave speed = frequency × wavelength
Sample questions
Written for this site in the style of AQA exam questions. They are not taken from real past papers.
Question 1Easy6 marks
A student makes waves in a tray of water by dipping a ruler into the water at regular intervals.
(a) The student dips the ruler into the water 15 times in 5.0 seconds. Each dip makes one wave. Calculate the frequency of the waves.[2]
(b) Calculate the period of the waves. Use the equation: \(\text{period} = \dfrac{1}{\text{frequency}}\)[2]
(c) The student now dips the ruler into the water more often. What happens to the frequency and to the period of the waves?[2]
Show the answer and mark scheme
(a)Answer: 3.0 Hz
15 ÷ 5.0
3.0 (Hz)
(b)Answer: 0.33 s
period = 1 ÷ 3.0
0.33 (s)
(c)Answer: The frequency increases and the period decreases.
the frequency increases
the period decreases
Question 2Medium9 marks
A student uses a ripple tank to investigate water waves. A lamp above the tank makes a pattern of bright lines on a sheet of white paper below the tank. The pattern moves across the paper as the waves travel.
(a) The student measures the distance from the first bright line to the eleventh bright line. The distance is 27 cm. Calculate the wavelength of the waves.[2]
(b) Explain why the student measured across several waves rather than measuring one wavelength.[1]
(c) Write down the equation that links frequency, wavelength and wave speed.[1]
(d) The student counts 32 waves passing a point on the paper in 20 s. Calculate the speed of the waves in m/s.[4]
(e) Counting the waves is difficult because the pattern moves quickly. Suggest one way the student could improve the measurement of the frequency.[1]
Show the answer and mark scheme
(a)Answer: 2.7 cm
27 ÷ 10
2.7 (cm)
(b)Answer: It reduces the uncertainty in the measured wavelength.
one wavelength is small so its (percentage) uncertainty would be large / measuring many waves and dividing reduces the uncertainty in the wavelength
(c)Answer: wave speed = frequency × wavelength
wave speed = frequency × wavelength
(d)Answer: 0.043 m/s (0.0432 m/s) m/s
frequency = 32 ÷ 20 = 1.6 (Hz)
wavelength = 0.027 m
v = 1.6 × 0.027
0.043 (m/s)
(e)Answer: Film the pattern and count the waves in slow motion (or use a stroboscope).
use a stroboscope to ‘freeze’ the pattern / film the waves and play the video back in slow motion / count the waves for a longer time