Identify wavefronts frequency and propagation speed
Separate a spatial front pattern from cycles counted at a fixed location.
Section P3.1 · General properties of waves
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
- Count complete repeated intervals.
- Read position and time axes separately.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
A time trace repeats after 0.50 s. What is its frequency?
What you will learn
- Describe wavefront, frequency and wave speed.
- Calculate frequency from complete cycles and distinguish a time trace from a spatial snapshot.
A wavefront joins matching parts of the wave
A wavefront is a line or surface joining points at the same stage of a wave cycle, such as a crest front in the chosen water-wave model. Straight fronts describe an approximately plane pattern; circular fronts describe spreading from a point in the tank view. A travel direction is normal to a front in these simple uniform-medium models.
Adjacent matching fronts are separated by a wavelength along that direction. A front is a pattern, not a container holding tagged particles. Wave speed is the rate at which a phase feature or the disturbance propagates through the stated medium; it is not the same as the instantaneous speed of a vibrating particle.
Count cycles at one place over time
Frequency f is the number of complete cycles per second at a fixed position, measured in hertz: 1 Hz means one cycle per second. If 12 complete cycles pass in 3.0 s, f = 12/3.0 = 4.0 Hz. The observation must count whole cycles consistently; twelve successive crest arrivals from the first to the twelfth span eleven intervals, not twelve.
A displacement–time graph follows one local point, so the time from one crest to the next is the period T. Frequency is 1/T for a regular wave. The supplied trace has a 0.50 s complete repeat, giving 2.0 Hz; its horizontal axis is time. No wavelength is measured directly from that trace without additional wave-speed or spatial information.
Sources for this lesson
Pause and explain
The first to sixth crest arrivals span 2.5 s. Which count should be divided by time?
Worked example
A regular wave gives 12 complete cycles at one point in 3.0 s. Find frequency and explain the observation location.
Show the worked solution
- Count complete cycles rather than only listed crest positions.
- Frequency = 12/3.0 = 4.0 cycles/s.
- The fixed-point observation measures repeated cycles over time.
Answer 4.0 Hz, measured by complete cycles at one fixed location.
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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.
Calculate frequency when 12 complete cycles pass one fixed point in 3.0 s.
Give me a hint
Divide the complete cycle count by elapsed time.
Compare my reasoning
- Use f = cycles/time.
- 12/3.0 = 4.0.
- State the rate as 4.0 Hz.
4.0 Hz.
Look for these in your work
- Count full cycles.
- Use seconds and hertz.
The first and ninth crest arrivals at one point are 4.0 s apart. Find frequency and period.
Give me a hint
Nine arrivals define eight complete intervals.
Compare my reasoning
- Eight cycles span 4.0 s.
- Frequency = 8/4.0 = 2.0 Hz.
- Period = 4.0/8 = 0.50 s.
2.0 Hz; period 0.50 s.
Look for these in your work
- Count intervals.
- Separate period and frequency.
A displacement–time trace has a 0.50 s repeat. Can its horizontal spacing alone establish wavelength?
Give me a hint
The axis describes one point over time, not many positions at once.
Compare my reasoning
- The repeat gives a period.
- Its reciprocal gives frequency.
- A spatial observation or wave speed is also needed to find wavelength.
No; it gives period and frequency, not wavelength directly.
Look for these in your work
- Read the axis meaning.
- Identify missing spatial information.
Common mistakes
- Hertz is cycles per second, not metres per second.
- Count intervals between recorded crest arrivals.
- A time trace does not directly show wavelength.
What can you explain now?
The first to sixth crest arrival spans 2.5 s. What is the frequency?
Compare with the explanation
2.0 Hz.
Five complete intervals occur in 2.5 s, giving 5/2.5 = 2.0 Hz.
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Make it stick
Describe a wavefront, count cycles at one place and distinguish propagation speed from local vibration.
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.