Read crests troughs amplitude and wavelength
Interpret a spatial wave snapshot with the undisturbed position as the reference.
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Read a labelled axis and unit scale.
- Distinguish a displacement from a distance along the wave.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
A wave ranges from −3 cm to +3 cm about zero. What is its amplitude?
What you will learn
- Describe crest, trough, amplitude and wavelength.
- Read repeated spatial features without using peak-to-trough height as amplitude.
Use the undisturbed position for amplitude
A spatial snapshot shows the displacement of a transverse medium against position at one instant. A crest is a maximum positive displacement and a trough is a maximum negative displacement relative to the chosen undisturbed line. Amplitude is the maximum displacement magnitude from that line, not the entire crest-to-trough separation.
In the supplied symmetric teaching wave, crests are +3 cm and troughs −3 cm, so amplitude is 3 cm and the full crest-to-trough difference is 6 cm. The sign describes displacement direction. The amplitude magnitude is non-negative; it is not a wave speed, travelled distance or frequency.
Measure a complete spatial repeat
Wavelength λ is the distance between adjacent points in the same part of the repeating cycle, such as adjacent crests or adjacent troughs. From a crest to its next trough is only half a wavelength for the symmetric sinusoidal model. A wavelength is measured along the propagation direction, not by following the curved rope's arc length.
If neighbouring crests are at x = 0.20 m and 0.80 m, wavelength is 0.60 m. Over several full wavelengths, divide the total corresponding distance by the number of complete repeats: from the first to the fourth crest spans three wavelengths. The snapshot does not show time passing, so its horizontal position axis cannot by itself give frequency.
Sources for this lesson
Pause and explain
First to fourth crest distance is 1.8 m. How many wavelengths does it contain?
Worked example
A spatial wave has crests +3 cm, troughs −3 cm and adjacent crests at 0.20 m and 0.80 m. Find amplitude and wavelength.
Show the worked solution
- Amplitude is the magnitude from the undisturbed line to a crest: 3 cm.
- Crest-to-trough height is 6 cm, not the amplitude.
- Wavelength = 0.80 − 0.20 = 0.60 m.
Answer Amplitude 3 cm; wavelength 0.60 m.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Read amplitude and wavelength from +3 cm/−3 cm displacements and crests at 0.20 and 0.80 m.
Give me a hint
Use the reference line and one complete spatial repeat.
Compare my reasoning
- Maximum displacement magnitude is 3 cm.
- Adjacent-crest separation is 0.80 − 0.20 m.
- Wavelength is 0.60 m.
3 cm; 0.60 m.
Look for these in your work
- Separate vertical and horizontal measurements.
- Use their stated units.
A wave's full crest-to-trough height is 8 mm and its first to fifth crest spans 1.2 m. Find amplitude and wavelength.
Give me a hint
The symmetric height is twice amplitude and five crests give four intervals.
Compare my reasoning
- Amplitude = 8/2 = 4 mm.
- The distance spans four full wavelengths.
- Wavelength = 1.2/4 = 0.30 m.
Amplitude 4 mm; wavelength 0.30 m.
Look for these in your work
- Count complete intervals.
- Do not confuse amplitude and wavelength.
A student reads 0.30 m along a snapshot's position axis and calls it a period of 0.30 s. Evaluate the claim.
Give me a hint
Identify what the axis measures before assigning a quantity.
Compare my reasoning
- The horizontal axis is position in metres.
- A period is a time for a complete cycle.
- A separate time observation is required; relabelling metres as seconds is invalid.
No period follows from that position reading alone.
Look for these in your work
- Use the axis meaning.
- Reject a unit relabelling.
Common mistakes
- Use the undisturbed line for amplitude.
- Crest to next trough is half a wavelength in this model.
- A spatial snapshot's axis is position, not elapsed time.
What can you explain now?
The first to fourth crest spans 1.8 m. What is the wavelength?
Compare with the explanation
0.60 m.
There are three complete crest-to-crest intervals, so divide 1.8 by three.
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Make it stick
Read amplitude and wavelength from correctly labelled spatial axes and count complete repeated intervals.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.