Rearrange wave speed equations and check supplied data
Find frequency or wavelength and test whether a supplied set is internally consistent.
Section 3.1 · General properties of waves
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 with consistent units.
- Rearrange a product equation.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which rearrangement finds wavelength?
What you will learn
- Use λ = v/f and f = v/λ.
- Check supplied speed, wavelength and frequency against one common wave model.
Choose the unknown before substituting
If speed and frequency are known, divide speed by frequency to find wavelength: λ = v/f. For v = 0.60 m/s and f = 4.0 Hz, λ = 0.15 m. If speed and wavelength are known, use f = v/λ; 340 m/s and 0.85 m give 400 Hz. The units supply a useful check on which division is appropriate.
Use positive frequencies and wavelengths for the ordinary scalar calculations here. A propagation direction is stated separately when needed. A negative displacement of the medium on a graph does not mean a negative wavelength or a negative number of cycles per second.
A set of three values must satisfy the same relation
Supplied values f = 5.0 Hz and λ = 0.12 m predict 0.60 m/s. If a claimed speed is 0.90 m/s under the same conditions, those three values are inconsistent. Identify the inconsistency rather than silently choosing a new wavelength or inventing an unreported change in medium.
In real observations, measurement uncertainty and changing conditions need to be considered. The exact supplied-data exercise is not a laboratory uncertainty assessment. Compare corresponding quantities under stated conditions and retain sensible precision; a rounded computed result alone cannot certify a student's measurement method or practical competence.
Pause and explain
With v = 340 m/s and λ = 0.85 m, which frequency follows?
Worked example
A wave travels at 340 m/s with wavelength 0.85 m. Find frequency.
Show the worked solution
- Rearrange v = fλ to f = v/λ.
- f = 340/0.85.
- Frequency is 400 Hz.
Answer 400 Hz.
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.
Find wavelength for v = 0.60 m/s and f = 4.0 Hz.
Give me a hint
Divide the speed by the cycle rate.
Compare my reasoning
- Use λ = v/f.
- 0.60/4.0 = 0.15.
- State wavelength as 0.15 m.
0.15 m.
Look for these in your work
- Use the correct division.
- State a length unit.
A wave travels at 300 m/s with wavelength 75 cm. Find frequency.
Give me a hint
Convert centimetres before dividing the speed.
Compare my reasoning
- λ = 0.75 m.
- f = v/λ.
- 300/0.75 = 400 Hz.
400 Hz.
Look for these in your work
- Convert the length.
- Keep the frequency unit.
Test a claimed set f = 5.0 Hz, λ = 0.12 m, v = 0.90 m/s for one unchanged wave.
Give me a hint
Compute the speed implied by the two other values.
Compare my reasoning
- fλ = 5.0 × 0.12 = 0.60 m/s.
- That differs from 0.90 m/s.
- The exact supplied set is inconsistent; a changed condition or measurement account would need evidence.
Inconsistent: the supplied frequency and wavelength predict 0.60 m/s.
Look for these in your work
- Check the relation independently.
- Do not invent a repair.
Common mistakes
- Identify the required unknown before dividing.
- Negative displacement does not create negative wavelength.
- Do not repair inconsistent supplied values without saying so.
What can you explain now?
Can f = 5.0 Hz, λ = 0.12 m and v = 0.90 m/s all describe the same supplied regular wave?
Compare with the explanation
No; fλ = 0.60 m/s.
The product disagrees with the claimed 0.90 m/s under the same conditions.
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Make it stick
Rearrange v = fλ for either unknown and test a supplied three-value set explicitly.
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.