Explain refraction through a change of wave speed
Keep source frequency while relating transmitted speed, wavelength and direction at a boundary.
Exam scope and assessment notes
Core and Extended · Physics 0972, 2026–2028, section 3.1. Core covers energy transfer, rope/spring/water-wave observations, wave features, speed, transverse and longitudinal models, reflection, refraction and ripple-tank diffraction. Extended compares wavelength effects at gaps and edges, including gap size. Written work is self-checked; human subject-teacher review, supervised practical competence and cumulative assessment remain pending. Cambridge states that IGCSE 0972 has the same subject content as IGCSE 0625, with 9–1 grading. This StudyForA pathway maps the 2026–2028 syllabus only. This 9–1 graded qualification is available only in a limited number of administrative zones. Confirm that your centre can enter you for this code and exam series with Cambridge International. Cambridge has published a separate syllabus for 2029. StudyForA has not reconciled that version yet; this page supports exams in 2026, 2027 and 2028 only.
Before you begin
- Use v = fλ.
- Measure propagation direction relative to a boundary normal.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which quantity stays unchanged for a stationary source and stationary boundary?
What you will learn
- Describe refraction due to a change in speed.
- Explain wavelength changes and normal-incidence limits for a stationary boundary.
A stationary boundary preserves the driving frequency
Refraction occurs when a transmitted wave changes speed as it enters a region with different propagation conditions. With a stationary source and stationary boundary, frequency is unchanged: successive cycles must cross the boundary at the source's rate. The new wavelength follows λ = v/f. A lower transmitted speed therefore gives a shorter wavelength for the same frequency.
For a supplied wave at 4.0 Hz, a speed change from 0.60 to 0.40 m/s changes wavelength from 0.15 to 0.10 m. The medium change does not create extra cycles per second at that stationary boundary. Do not keep the original wavelength while changing speed and claiming frequency also stays the same.
Direction depends on incidence as well as speed
For oblique incidence in the simple isotropic model, entry into the slower region bends the propagation direction toward the normal; entry into the faster region bends it away. Wavefronts rotate accordingly and remain perpendicular to the transmitted propagation direction. The supplied illustration chooses directions and wavelength spacing consistent with one stationary-boundary model, not a measured tank result.
At normal incidence, a wave can change speed and wavelength without changing direction. Therefore 'refraction' must not be reduced to 'every boundary always bends the path'. In suitable ripple-tank conditions, water waves slow over a shallow region and their spacing decreases at fixed source frequency. Use the stated depth and wave conditions rather than declaring one universal speed for all water waves.
Pause and explain
A 4.0 Hz transmitted wave has speed 0.40 m/s. What wavelength follows?
Worked example
At a stationary boundary, a 4.0 Hz wave slows from 0.60 to 0.40 m/s. Find both wavelengths and the oblique direction trend.
Show the worked solution
- Initial λ = 0.60/4.0 = 0.15 m.
- Transmitted λ = 0.40/4.0 = 0.10 m with unchanged frequency.
- For the stated oblique model, the slower-region direction is closer to the normal.
Answer 0.15 m then 0.10 m; frequency unchanged; oblique ray bends toward the normal.
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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.
Find wavelengths before and after a 4.0 Hz wave slows from 0.60 to 0.40 m/s.
Give me a hint
Use the same frequency on each side of the stationary boundary.
Compare my reasoning
- Initial wavelength is 0.60/4.0 = 0.15 m.
- Transmitted wavelength is 0.40/4.0 = 0.10 m.
- The shorter spacing accompanies the lower speed.
0.15 m and 0.10 m; frequency remains 4.0 Hz.
Look for these in your work
- Use each region's speed.
- Keep the boundary condition.
A stationary-boundary wave at 5.0 Hz speeds up from 0.20 to 0.30 m/s. Find wavelengths and the oblique direction trend.
Give me a hint
Use λ = v/f and reverse the slower-region direction trend.
Compare my reasoning
- Initial wavelength = 0.20/5.0 = 0.040 m.
- Transmitted wavelength = 0.30/5.0 = 0.060 m.
- For the stated oblique model, entry into the faster region bends away from the normal.
0.040 m then 0.060 m; oblique direction bends away from the normal.
Look for these in your work
- Calculate both repeats.
- State the incidence condition.
A normally incident wave has a shorter wavelength after entering a slower region. A student says no refraction occurred because the path did not bend. Evaluate.
Give me a hint
Direction is only one possible changed property.
Compare my reasoning
- The incident direction is normal to the boundary.
- Speed and wavelength still change.
- Refraction occurs without a direction change in this normal-incidence case.
Refraction can occur at normal incidence without bending the path.
Look for these in your work
- Retain the normal-incidence case.
- Identify the speed change.
Common mistakes
- Stationary-boundary frequency is unchanged.
- A lower speed at fixed frequency means a shorter wavelength.
- Normal incidence can keep direction unchanged despite refraction.
What can you explain now?
A normally incident wave slows at a stationary boundary. Must its path bend?
Compare with the explanation
No.
Speed and wavelength can change while the normal-aligned propagation direction stays the same.
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Make it stick
Explain stationary-boundary refraction using unchanged frequency, changed wavelength and explicit incidence direction.
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