Rearrange wave speed equations and check supplied data
Find frequency or wavelength and test whether a supplied set is internally consistent.
Section P3.1 · General properties of waves
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
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.
Sources for this lesson
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.
After trying it yourself, choose your next review. This is your self-assessment.
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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.