Wave Terms
Measure amplitude, wavelength and frequency from a wave diagram, with the correct units.
On this page
Wave · about 25–35 min
What you need to understand
Amplitude is one-sided; wavelength is a distance; frequency is cycles per second.
Definitions
- amplitude
the maximum displacement from the equilibrium position
For example: Measure from the middle line to a crest, not crest to trough.- frequency
the number of complete cycles each second
For example: Three cycles per second is 3 Hz.- wavelength
the distance between consecutive points in the same phase
For example: Crest-to-crest distance is one wavelength.
Key idea
- LookInspect the wave drawing: amplitude is marked from equilibrium to a crest, wavelength between consecutive crests, and 12 complete cycles pass in 4 s. Read all three quantities.
- ThinkAmplitude is one-sided; wavelength is a distance; frequency is cycles per second.
- DoRead each wave quantity from the correct reference and include suitable units.
Explanation
Amplitude is the maximum displacement from the equilibrium line. Measure from the middle line to a crest or to a trough—not from crest to trough.
Frequency is the number of complete cycles each second and is measured in hertz (Hz). Wavelength is a distance between consecutive points at the same stage of a cycle, such as crest to crest, and is measured in metres or centimetres.
Pause and say it: Amplitude is one-sided; wavelength is a distance; frequency is cycles per second.
Common mistake
Tempting wrong idea: Amplitude is crest-to-trough distance.
Why it fails: Crest-to-trough is twice the amplitude because it includes displacement on both sides of the equilibrium line.
Use this instead: Amplitude is measured from equilibrium to a crest or trough, not from crest to trough.
Practical work
What to show: Read each wave quantity from the correct reference and include suitable units.
Before you finish: Do not report crest-to-trough distance as amplitude.
Practical: Measure a rope wave
How does hand vibration frequency affect the number of waves produced per second?
Safety: Keep the rope below waist height, maintain clear space and do not wrap it around a hand or body.
- Change
- hand oscillations per second
- Measure
- wave frequency and observed wavelength
- Keep the same
- same rope tension, same amplitude, same measured length
View the apparatus, method and sample results
Apparatus
long rope, floor markers, stopwatch, metre rule.
Method
Stretch the rope under steady, safe tension with a partner.
Mark the equilibrium line and a fixed observation length.
Produce ten regular oscillations while a partner times them.
Count wavelengths visible in the fixed length and measure crest-to-crest distance.
Repeat for a different oscillation rate and take three trials.
| Setting | Time for 10 oscillations / s | Frequency / Hz | Wavelength / m |
|---|---|---|---|
| slow | 8.0 | 1.25 | 1.2 |
| medium | 5.0 | 2.00 | 0.75 |
| fast | 4.0 | 2.50 | 0.60 |
Limitation: Rope tension and hand motion are difficult to keep exactly constant.
Improvement: Use a mechanical vibrator and measured hanging load to control frequency and tension.
6. Worked Examples
Modelled example 1
Read a wave
Problem
Inspect the wave drawing in section 2. Its amplitude arrow runs from equilibrium to a crest, its wavelength arrow joins consecutive crests, and 12 complete cycles pass in 4 s. Read amplitude and wavelength, then calculate frequency.
Study the worked solution
Reason from the evidence
Method
Read displacement from equilibrium for amplitude and divide cycle count by time for frequency.
Reason
Amplitude is one-sided; wavelength is a distance; frequency is cycles per second.
Working
- The equilibrium-to-crest arrow gives amplitude = 3 cm.
- The crest-to-crest arrow gives wavelength = 30 cm.
- Frequency = cycles ÷ time = 12 ÷ 4.
- Frequency = 3 Hz.
State the conclusion
Working
Amplitude = 3 cm, wavelength = 30 cm and frequency = 3 Hz.
Guided practice 2
Read three different wave quantities
Problem
A crest is 4 cm above equilibrium. Consecutive crests are 24 cm apart, and 18 cycles pass in 6 s. Find amplitude, wavelength and frequency.
Give each quantity with its unit
Hints
Hint 1: read the two distances
One distance begins at equilibrium; the other joins matching points.
Hint 2: find cycles per second
Divide 18 cycles by 6 s.
View solution step by step
Identify the spatial quantities
Method
Use equilibrium-to-crest for amplitude and crest-to-crest for wavelength.
Reason
The two quantities use different reference points.Working
amplitude = 4 cm; wavelength = 24 cmCalculate the frequency
Reason
Frequency is the number of complete cycles each second.
Working
frequency = 18 ÷ 6 = 3 Hz
Common misconception 3
Correct a doubled amplitude
Learner response
A wave extends 3 cm above and 3 cm below equilibrium. A learner reports an amplitude of 6 cm. Locate the error.
Name the correct reference points
View solution step by step
Use the definition
Method
Measure from equilibrium to one extreme.Reason
Amplitude is maximum displacement on one side of the equilibrium position.
Working
amplitude = 3 cm; crest-to-trough distance = 6 cm
Examiner practice 4
Determine amplitude, wavelength and frequency
Examination question
A wave has a crest 2.5 cm above equilibrium. Crests occur at 10 cm and 38 cm along a rope. Fifteen cycles pass a point in 5.0 s. Determine amplitude, wavelength and frequency. [4 marks]
Show the two required calculations
View solution step by step
Read amplitude
1 markMethod
Use the displacement above equilibrium.Reason
The value is already measured from the correct reference.
Working
amplitude = 2.5 cmFind wavelength
1 markMethod
Subtract consecutive crest positions.Reason
Wavelength is a separation, not a position from the origin.
Working
wavelength = 38 − 10 = 28 cmFind frequency
2 marksMethod
Divide complete cycles by time.Reason
This gives cycles per second.Working
frequency = 15 ÷ 5.0 = 3.0 Hz
Self-mark with the mark scheme
Compare your response with each mark point. Select a point only when your response contains that evidence.
Self-mark amplitude, wavelength method, frequency method and units.
Challenge 5
Complete a mixed wave-data record
Problem
A record gives: equilibrium-to-trough distance 1.8 cm; crest positions 12 cm and 32 cm; time for 20 cycles 8.0 s. Convert each observation into the correct named wave quantity.
Name, calculate and give units
Hints
Hint 1: name the direct reading
Equilibrium to an extreme is already one quantity.
Hint 2: process the other two
Subtract positions for one distance; divide cycles by time for the rate.
View solution step by step
Translate the three observations
Method
Match each observation to its definition before calculating.
Reason
This prevents distance, position and rate data from being mixed.
Working
amplitude = 1.8 cm; wavelength = 32 − 12 = 20 cm; frequency = 20 ÷ 8.0 = 2.5 Hz
Guided practice
Try it with support
A crest is 2.0 cm above equilibrium, 15 cycles pass in 5.0 s, and consecutive crests are at 8 cm and 28 cm. Find amplitude, frequency and wavelength.
Amplitude uses equilibrium to crest.
Frequency is cycles ÷ time.
Wavelength is the separation of matching points.
Check the guided answer
Answer: Amplitude = 2.0 cm, frequency = 15 ÷ 5.0 = 3.0 Hz, and wavelength = 28 − 8 = 20 cm.
Check: Each answer uses a different reference and unit.
Practise and continue
Practise this
The crest-to-trough distance is 8 cm and 24 cycles pass in 6 s. Find the amplitude and frequency.
Need a hint?
Crest to trough is twice the amplitude.
Check your answer
Answer: Amplitude = 8 ÷ 2 = 4 cm and frequency = 24 ÷ 6 = 4 Hz.
Check: Do not report crest-to-trough distance as amplitude.
Think like a scientist
Why is timing 20 cycles usually better than timing one cycle with the same stopwatch?
Check the reasoning
The same reaction-time uncertainty is a smaller fraction of a longer total time, so dividing by 20 gives a more reliable period or frequency estimate.
Remember: Repeating and averaging can reduce random variation further.
One-minute check
Hide the page and explain measure a wave correctly in your own words.
Give a new example that is different from the worked example.
Correct this common mistake: “Amplitude is crest-to-trough distance.”
Syllabus and review details
- SEC G1 Science 2027 · 2027
Content structure and syllabus content, PDF pages 8–17
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