Explain refraction through a change of wave speed
Keep source frequency while relating transmitted speed, wavelength and direction at a boundary.
Cross-referenced to the 2028–2029 0653 section using original teaching from the related single-science courses. A 0653-specific objective-by-objective and Core/Supplement review is in progress. Written practice is self-checked and does not demonstrate supervised laboratory competence or award an official Cambridge grade.
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.
Sources for this lesson
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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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.
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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