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AQA GCSE Physics · Topic 4.6 Waves
Wave Speed: v = f λ and v = s ÷ t
In this lesson you'll learn to: use the wave equation v = f × λ and explain where it comes from,
use v = s ÷ t for a wave that travels a measured distance, spot when a wave goes there and back
(echoes, ultrasound, reflected light), convert cm, minutes and kHz before you calculate, and pick the right
formula for the question.
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Prefer to watch? Scroll to the bottom for the video on this topic
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A video walkthrough is coming soon — it will appear at the bottom of this page
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Start here — have a play
Don't read anything yet. On tab 1, pick a frequency and a wavelength, then predict how far the wave will get in one second before you press Run. On tab 2, time five different waves and see which ones go there and back. Tab 3 tests whether you can choose the right formula.
Frequency f
Wavelength λ
Why v = f × λ? Frequency is the number of waves made each second. Each wave is one wavelength long. So in one second the wave travels (number of waves) × (length of each) = f × λ metres. Metres travelled in one second is the speed.
Echo, sonar, ultrasound, laser reflection? The wave goes there and back, so the distance it travels is 2 × the distance to the object. Light from the Sun only goes one way.
Which formula?
The test: given a frequency or a wavelength? Use v = f × λ. Given a distance and a time? Use v = s ÷ t. Then check whether it went there and back.
Waves in tab 1 are slowed down. Real sound waves vibrate hundreds of times a second.
▲ Three tabs: v = f × λ wave by wave, v = s ÷ t with a stopwatch, then "which formula?"
Two formulas, one speed. Now learn when to use each.
The notes below have both formulas with their units, the "there and back" rule, and the unit changes that cost marks every year.
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Revision notes
The two wave speed formulas
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v = f × λ
wave speed = frequency × wavelength
v in m/s · f in Hz · λ in m⏱
v = s ÷ t
wave speed = distance ÷ time
v in m/s · s in m · t in sYou need to recall v = f × λ (it's on the AQA equation list you must learn) and apply it. Rearranged: f = v ÷ λ and λ = v ÷ f. Rearranging v = s ÷ t gives t = s ÷ v and s = v × t.
⭐ Why v = f × λ works
Frequency is the number of waves made each second. Each wave is one wavelength long. So in one second the wave travels f × λ metres, and the metres travelled in one second is the speed.
Example: 2 Hz and λ = 1.5 m. Two waves a second, each 1.5 m long, so the wave travels 3.0 m every second: v = 3.0 m/s.
Which formula?
| The question gives you… | Use | Typical example |
|---|---|---|
| a frequency and/or a wavelength | v = f × λ | a note of 425 Hz, wavelength 0.80 m |
| a distance and/or a time | v = s ÷ t | an echo, a ripple timed across a tank, light from the Sun |
⭐ There and back: double the distance
An echo, a sonar pulse, an ultrasound scan or a laser bounced off the Moon all reflect. The wave goes to the object and back, so s = 2 × the distance to the object.
If you're asked for the depth or the distance to the object, work out s = v × t, then halve it. Light from the Sun, or thunder reaching you, only goes one way.
Change the units first
| If it's in… | Change it to… | How |
|---|---|---|
| cm | m | ÷ 100 (4.0 cm = 0.040 m) |
| mm | m | ÷ 1000 |
| km | m | × 1000 |
| minutes | s | × 60 |
| kHz / MHz | Hz | × 1000 / × 1 000 000 |
Speeds worth knowing
| Wave | Roughly |
|---|---|
| Ripples in a ripple tank | about 0.1 – 0.3 m/s |
| Sound in air | about 330 – 340 m/s |
| Sound (and ultrasound) in water and the body | about 1500 m/s |
| Light and all electromagnetic waves (in a vacuum) | 3.0 × 10⁸ m/s |
A question always gives you the speed if it's needed, but these help you spot a wrong answer. Sound at 34 m/s or light at 3 m/s means a slip somewhere.
⭐ Measuring the speed of sound in air (the spec asks you to describe a method)
Stand a measured distance from a large wall (say 50 m, measured with a trundle wheel). Clap and time how long the echo takes with a stopwatch. Better: clap in time with the echoes and time 20 claps, then divide. The sound goes there and back, so v = (2 × 50) ÷ t.
Measuring the speed of ripples is Required Practical 8, on the next page of the workbook.
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How to write it in the exam
Every wave speed calculation, the same three steps
Write the equation →
put the numbers in, in m, s and Hz →
give the answer with its unit.
1 mark for the right equationconvert firstunit, m/s
Workbook page 5 · the water wave · 2 sig figs
The graph shows a water wave with a wavelength of 4 cm. Its frequency is 5 Hz. Calculate its speed in m/s.
Workbook page 5: everything on the graph is in cm
- Wavelength = 4.0 cm = 0.040 m (everything on the graph is in cm)
- v = f × λ = 5 × 0.040
- v = 0.20 m/s
Workbook page 5 · echo off a cliff · 7 marks
Girls sing a note of frequency 425 Hz and wavelength 0.80 m. They stand 300 m from a cliff and hear an echo.
(c) either ray diagram scores: at a small angle, i = r
…or straight back along the normal
- (a) v = f × λ = 425 × 0.80 = 340 m/s [2]
- (b) The echo is the sound wave reflected off the cliff [1]
- (c) Ray diagram: a ray to the cliff and back, with the angle of incidence = angle of reflection (or straight back along the normal), arrows towards and away from the cliff [1]
- (d) Distance = 300 × 2 = 600 m (to the cliff and back) · t = s ÷ v = 600 ÷ 340 = 1.76 s ≈ 1.8 s [3]
Where marks go missing: using 300 m gives 0.88 s. That's only the time to reach the cliff, not there and back.
Workbook page 6 · Question 1(a) · 2 marks
The graph shows a water wave in a ripple tank at one instant in time. (i) What is the wavelength? (ii) What is the amplitude?
Workbook page 6, Q1(a): the x-axis is in m, the y-axis in cm
- (i) Wavelength = C 0.8 m, peak to the next peak. (A is a quarter of a wavelength, B is half, D is two wavelengths.)
- (ii) Amplitude = B 6 cm, middle line to the peak. (C, 12 cm, is peak to trough.)
Workbook page 6 · Question 1(b) and (c) · the buoy · 11 marks
A buoy on the sea moves up and down between level X and level Y.
Q1(b): W is one wavelength; X to Y is peak to trough
- (i) W = a horizontal line between two matching points, e.g. peak to the next peak [1]
- (ii) X to Y = 1.2 m is peak to trough, so amplitude = 1.2 ÷ 2 = 0.6 m [1]
- (iii) The buoy reaches X every 4.0 s, so T = 4.0 s. f = 1 ÷ T = 1 ÷ 4.0 = 0.25 Hz [3: working, answer, unit]
- (iv) v = f × λ = 0.25 × 6.0 = 1.5 m/s [2]
- (v) The buoy oscillates up and down, which is perpendicular to the direction the wave travels (the direction of energy transfer) [2]
- (vi) The wave transfers energy (not water, and not the buoy) [1]
- (c) A longitudinal wave: sound (or ultrasound) [1]
The chain: time between two highest points = period → f = 1 ÷ T → then v = f × λ.
Worked example · light from the Sun · 3 marks
The Sun is 1.5 × 10¹¹ m from the Earth. Light travels at 3.0 × 10⁸ m/s. How long does sunlight take to reach us?
- One way only, so s = 1.5 × 10¹¹ m
- t = s ÷ v = 1.5 × 10¹¹ ÷ 3.0 × 10⁸ = 500 s
- 500 ÷ 60 = 8 minutes 20 seconds
Worked example · ultrasound depth · 3 marks
An ultrasound pulse travels at 1500 m/s in the body. The echo from an organ returns after 0.000080 s. How deep is the organ?
- s = v × t = 1500 × 0.000080 = 0.12 m (there and back)
- Depth = 0.12 ÷ 2 = 0.060 m (6.0 cm)
📘 Now do it in your workbook
Page 5: write both formulas with their units, calculate the speed of a water wave from a graph, and the echo-off-a-cliff exam question. Page 6: a full 13-mark exam question on wave types, properties and formulas.
AQA GCSE Physics Workbook · WAVES · pages 5 and 6The full workbook covers the whole of Topic 4.6 Waves, with exam-style questions and worked answers.
✅ Can you do it? Tick as you go
0% complete🎉 Nice work! You've ticked off every objective for this spec point.
Don't forget to hit “Mark complete” at the bottom of the lesson.
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Prefer to watch? Here's the whole thing
Video walkthrough — coming soon
Everything above, explained out loud — useful for a last-minute recap, or if you'd rather hear it than read it.
Everything above, explained out loud — useful for a last-minute recap, or if you'd rather hear it than read it. The video is on its way.
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Video coming soon
The walkthrough for this lesson is being filmed and will appear right here. Until then, the animation and the notes above cover every mark.
Now put it into practice
Pages 5 and 6 of the workbook have both formulas, the water-wave graph, the echo question and a full 13-mark exam question, with answers at the back.
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