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Wave speed, frequency and wavelength practice
For a periodic traveling wave, speed equals frequency times wavelength: v = fλ. Frequency counts cycles per second; wavelength is the distance between corresponding points in neighboring cycles.
By ExamCat · Original study lesson · Published September 24, 2026
Understand the method
Keep units consistent. Hertz means s⁻¹, so Hz multiplied by meters produces m/s. Period is the duration of one cycle and equals 1/f. Wave speed depends on the medium and wave type, not simply on how fast you wiggle the source.
Worked example, step by step
A wave travels at 24 m/s with frequency 6 Hz. Find wavelength and period.
- Rearrange λ = v/f = 24/6 = 4 m.
- Find period T = 1/f = 1/6 s ≈ 0.167 s.
- Check that traveling one wavelength takes 4/24 s, the same period.
- If frequency doubles while speed stays 24 m/s, wavelength becomes 2 m.
A mistake to watch for
Amplitude is not wavelength. Increasing the height of a wave does not mean that adjacent crests are farther apart. State what remains fixed before predicting how one quantity changes.
Try it yourself: three questions
Write an answer before opening the explanation. For calculations, keep your units and intermediate steps; for concepts, state the reason for your choice.
1. A wave has f = 5 Hz and λ = 3 m. Find speed.
Show answer and explanation
15 m/s. There are five wavelengths passing a point each second.
2. A period is 0.25 s. Find frequency.
Show answer and explanation
4 Hz, because four cycles fit in one second.
3. At a boundary, frequency stays fixed but speed decreases. What happens to wavelength?
Show answer and explanation
It decreases proportionally because λ = v/f. This follows only after specifying the fixed frequency.
Build your next practice session
Mark the first step where your reasoning differed from the explanation. Turn that step into a question, answer it without looking, then change one condition in the example and explain what would change. A correct guess is a reason to revisit the method.
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Further reading
OpenStax Physics provides textbook background. The worked scenario and practice questions on this page were written independently for ExamCat.
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