Compare wavelength and gap size in diffraction
Vary one quantity at a time and relate relative spreading to wavelength compared with the opening.
Section P3.1 · General wave properties
Cross-referenced from the related Cambridge IGCSE Chemistry 0620 or Physics 0625 teaching to the 0652 syllabus. Exact 0652 Core/Supplement objective coverage and this final-series course’s examiner fit still need specialist review. Written practice is self-checked and does not predict a Cambridge grade or demonstrate supervised laboratory competence.
Before you begin
- Describe gap diffraction and use v = fλ.
- Recognise a fair comparison with one changed variable.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
At fixed wavelength, what happens to relative spreading when a gap becomes much narrower?
What you will learn
- Describe how wavelength and gap size affect gap diffraction.
- Make separate controlled comparisons without inferring exact angles or transmission amounts.
Compare gap width with wavelength
Diffraction spreading is more pronounced when a gap is small compared with wavelength or comparable with it, and less pronounced when the gap is much wider than wavelength. At fixed wavelength, reducing the gap width increases the relative spread of the transmitted pattern. A wide-gap pattern can still show spreading near its edges; it is too absolute to call every wide-gap case zero diffraction.
At fixed gap width, increasing wavelength makes spreading more pronounced; decreasing wavelength makes it less pronounced. These are separate controls. The dimensionless comparison gap width/wavelength helps rank supplied situations, but it is not a syllabus formula giving an exact spreading angle or transmitted energy fraction.
Change one cause at a time
For a supplied 4.0 cm gap, wavelengths 1.0 and 4.0 cm give ratios 4 and 1. The 4.0 cm wavelength gives stronger spreading in the stated matched comparison. At fixed wavelength 2.0 cm, gaps 2.0 and 8.0 cm give ratios 1 and 4; the smaller gap has stronger spreading. These are original supplied teaching values rather than measured tank data.
A ripple-tank investigation can compare gaps at a fixed source and depth, or compare wavelengths while retaining the gap and documenting the propagation conditions. If speed is supplied constant, reducing frequency increases wavelength by λ = v/f. Real water waves can have speed conditions that depend on their wave regime, so a frequency change alone must not be treated as an unmeasured universal guarantee of unchanged water-wave speed.
Sources for this lesson
Pause and explain
For one 4.0 cm gap, which wavelength gives more spreading: 1.0 or 4.0 cm?
Worked example
A 4.0 cm gap is compared with 1.0 cm and 4.0 cm wavelengths under matched conditions. Which gives more pronounced spreading?
Show the worked solution
- Gap/wavelength ratios are 4.0/1.0 = 4 and 4.0/4.0 = 1.
- The latter wavelength is comparable with the gap.
- The 4.0 cm wavelength therefore gives more pronounced spreading in the stated comparison.
Answer The 4.0 cm wavelength gives stronger spreading; ratios are 4 and 1.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
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.
Compare diffraction for a 4.0 cm gap with wavelengths 1.0 and 4.0 cm.
Give me a hint
Express the same gap in units of each wavelength.
Compare my reasoning
- Ratios are 4 and 1.
- The longer wavelength is comparable with the gap.
- It gives more pronounced spreading under matched conditions.
4.0 cm wavelength gives more spreading; ratios 4 and 1.
Look for these in your work
- Hold gap fixed.
- Explain the relative-size comparison.
At fixed 2.0 cm wavelength, compare gaps 2.0 and 8.0 cm.
Give me a hint
Keep wavelength fixed and compare the two opening ratios.
Compare my reasoning
- The ratios are 1 and 4.
- The 2.0 cm opening is comparable with wavelength.
- It gives greater relative spreading than the 8.0 cm opening.
2.0 cm gap gives more spreading; ratios 1 and 4.
Look for these in your work
- Hold wavelength fixed.
- Avoid claiming zero wide-gap diffraction.
A constant-speed supplied wave at 0.40 m/s changes from 20 to 10 Hz through the same 4.0 cm gap. Find wavelengths and compare spreading.
Give me a hint
Use the explicitly supplied constant speed, then compare opening ratios.
Compare my reasoning
- Wavelengths are 0.40/20 = 0.020 m and 0.40/10 = 0.040 m.
- Those are 2.0 and 4.0 cm, giving gap/wavelength ratios 2 and 1.
- The 10 Hz case has the longer wavelength and stronger spreading under these supplied conditions.
2.0 cm then 4.0 cm; the 10 Hz case spreads more.
Look for these in your work
- Retain the supplied speed condition.
- Do not infer an energy percentage.
Common mistakes
- Compare gap width relative to wavelength.
- Change only the intended variable in a fair comparison.
- More spreading is not automatically more transmitted energy.
What can you explain now?
At fixed 2.0 cm wavelength, which gap gives more spreading: 2.0 or 8.0 cm?
Compare with the explanation
The 2.0 cm gap.
It is comparable with wavelength, whereas the 8.0 cm opening is four wavelengths wide.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Compare wavelength and gap separately, use relative size and retain the limits of a qualitative spread prediction.
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.