Describe progressive waves and wave quantities
Describe how a progressive disturbance travels and use displacement, amplitude, phase, period, frequency and wavelength.
Section 7 · Waves
AS Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 7. These original wave examples and diagrams are conceptual study aids; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use frequency, period, wavelength, amplitude, speed and trigonometric ratios with consistent units.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What does a progressive wave transfer from place to place?
What you will learn
- Describe progressive wave motion using ropes, springs or ripple tanks
- Define displacement, amplitude, phase difference, period, frequency, wavelength and speed
- Explain that a progressive wave transfers energy
A progressive wave carries a disturbance through a medium or space
Wave motion can be seen in a pulse travelling along a rope, compressions moving along a spring, or ripples spreading across water. Points in the medium oscillate about equilibrium while the wave pattern progresses.
A progressive wave transfers energy from one place to another. In a simple travelling-wave model, the medium's particles or points oscillate locally; they do not travel forward with the wave as a whole.
Describe the pattern with linked quantities
Displacement is a point's signed distance from equilibrium. Amplitude is the maximum magnitude of that displacement. Period T is the time for one cycle, frequency f is the number of cycles per second, and wavelength λ is the distance between adjacent points in phase.
Phase difference compares cycle positions. One complete cycle is 2π radians or 360°. For a travelling wave, adjacent points one wavelength apart are in phase; points half a wavelength apart are in antiphase. Wave speed describes how quickly a fixed phase point advances.
Pause and explain
What is the period of a wave?
Worked example
A source makes 12 complete oscillations in 3.0 s. Find its frequency and period.
Show the worked solution
- Frequency = number of cycles / time = 12/3.0 = 4.0 Hz.
- Period T = 1/f = 1/4.0.
- Check that period is in seconds and frequency in hertz.
Answer Frequency 4.0 Hz; period 0.25 s.
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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.
A water-wave source oscillates 18 times in 6.0 s. Find its frequency and period.
Give me a hint
Calculate cycles per second first, then take the reciprocal.
Compare my reasoning
- f = 18/6.0 = 3.0 Hz.
- T = 1/f = 1/3.0 s.
- Give both units.
f = 3.0 Hz; T ≈ 0.33 s.
Look for these in your work
- Frequency calculated
- Period is reciprocal
- Units stated
The maximum displacement of a point on a wave is 4.0 cm. What is its amplitude, and what is its peak-to-peak displacement?
Give me a hint
Amplitude is the maximum distance from equilibrium.
Compare my reasoning
- Amplitude = 4.0 cm.
- Peak-to-peak displacement is twice the amplitude.
- Calculate 2 × 4.0 cm.
Amplitude 4.0 cm; peak-to-peak displacement 8.0 cm.
Look for these in your work
- Amplitude defined from equilibrium
- Peak-to-peak distinguished
- Both values and units stated
Two points on a travelling wave are separated by half a wavelength. State their phase difference in degrees and describe their relative displacements at the same instant.
Give me a hint
A full wavelength corresponds to one full 360° cycle.
Compare my reasoning
- Half a wavelength is half a cycle.
- Phase difference = 180°.
- The points are in antiphase, so their displacements are opposite at the same instant in an ideal sinusoidal wave.
180° phase difference; the points are in antiphase and have opposite displacements at the same instant.
Look for these in your work
- Wavelength-to-cycle relation used
- Angle calculated
- Antiphase interpreted
Common mistakes
- Saying the particles travel along with the wave in the simple travelling-wave model
- Confusing amplitude with peak-to-peak displacement
- Calling frequency the time for one cycle
What can you explain now?
What does a progressive wave transfer from place to place?
Compare with the explanation
Energy
The disturbance carries energy as it progresses.
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Make it stick
How can a wave transfer energy while points in its medium oscillate locally?
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