Measuring waves
Key idea: Measure across several wavelengths and time several cycles, then divide by the interval counts. Multiply the same wave's frequency and wavelength to find its speed.
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Guided lessons · coming soon
Guided lesson
Guided steps
- Measure between matching phases and count complete intervals.
- Count the gaps before calculating a wavelength.
- Compare seconds per cycle with cycles per second.
- Calculate period and frequency, then choose why a longer timing helps.
- Keep spatial and timing evidence with the same wave and medium conditions.
- Follow how matched distance and timing measurements give wave speed.
- Calculate each setting separately and reject the mixed evidence.
- Combine interval counting and cycle timing for the complete changed case.
- Recover phase, interval and matching checks before using wave apparatus.
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ContinueA still picture shows where a wave pattern repeats. Timing shows when it repeats. Use a spatial measurement for wavelength and a timing measurement for frequency; neither can replace the other.
Measure a repeat distance
Measure between points in the same phase, such as neighbouring crests or the centres of neighbouring compressions. For a longer span, count complete intervals and divide the distance by that count. Six crest positions enclose five intervals, not six.
The rope and particle models show repeat distances at one instant. The displacement of a particle is not the distance the wave pattern travels. In a ripple tank, use an appropriate projected image or scale to avoid parallax, and account for magnification if the instructions require it.
Spot the mistake 1
Six crests are not six wavelengths
Problem
A photograph shows six successive crests from the first at 0.00 m to the sixth at 0.40 m. A learner divides 0.40 m by six. Count the complete wavelength intervals and correct the wavelength calculation.
Try before revealing the solution
Show the steps Optional working
Show solution step by step
Count gaps
Method
Count the repeat distances between the first and last crests.
Reason
Six crest positions enclose five crest-to-crest intervals.
Working
Answer
There are five complete wavelengths in the 0.40 m span.
Use the correct divisor
Method
Divide by five, not six.Reason
The divisor is the number of intervals actually measured.
Working
Answer
λ = 0.40/5 = 0.080 m. Five × 0.080 m recovers the full 0.40 m span.
Common mistake
For timing, make the same distinction: the first event starts the interval count at zero. State which events bound the measurement.
Time complete cycles
Observe a marked point or a clearly identifiable phase of the pattern. Start counting at zero when timing begins, then count complete cycles. For N cycles in time t:
Timing several cycles reduces the relative effect of start/stop uncertainty. Repeat and compare, but check the interval count: repeating the same counting mistake will not remove it.
Guided practice 2
Find a period from repeated cycles
Problem
A marker completes 20 cycles in 8.0 s. Find its period and frequency. Choose why timing one cycle with a hand-operated stopwatch is usually a poorer choice.
Try before revealing the solution
Hints
Hint 1
Find the decisive relationship
Which quantity measures time per cycle, and which counts cycles per second?
Show solution step by step
Divide elapsed time by cycles
Method
Calculate the time for one cycle.Reason
Period is seconds per cycle, the inverse of frequency.
Working
Answer
T = 8.0 s/20 = 0.40 s; f = 1/T = 2.5 Hz.Reduce the relative timing effect
Method
Use an identifiable phase and time several complete cycles.
Reason
A similar start/stop reaction uncertainty is a smaller fraction of a longer elapsed time.
Working
Answer
Begin counting at zero at a chosen phase, stop after 20 complete cycles, repeat and compare. Repetition cannot correct consistently counting the wrong number of cycles.
Quick check
The display resolution is only one part of the timing uncertainty. Follow the apparatus and recording instructions.
Match measurements before calculating speed
Use wavelength and frequency for the same steady wave under the same medium conditions:
Keep water depth fixed when investigating a ripple-tank frequency change. If a direct speed method is supplied, time a matching travel distance for an identifiable wavefront and compare it with the frequency–wavelength result. Do not mistake local vibration speed for wave speed.
Keep water clear of electrical connections and follow instructions for lamps, vibrating sources and viewing equipment. Use the supplied viewing method; do not improvise flashing-light settings. Wave measurements still need supervised equipment practice.
Determination of the speed, wavelength and frequency of waves
Method
Measure several wavelengths across a wave pattern and divide by the number of intervals. Determine frequency from counted cycles per measured time, then calculate speed using v = fλ; repeat under fixed medium conditions.
Why it works
Using multiple spatial intervals and cycles reduces percentage uncertainty. Wavelength and frequency must describe the same steady wave in the same medium before they are combined.
A mistake to avoid: Wave speed is found by adding frequency and wavelength.
Check your understanding
How does measuring across several wavelengths and timing several cycles reduce percentage uncertainty?
Show answer
A similar endpoint or start/stop uncertainty is a smaller fraction of a longer measured span or time. Divide a spatial span by its complete wavelength intervals; divide complete cycles by elapsed time for frequency. Match both measurements to the same steady wave.
Worked example 3
Combine matching wavelength and frequency
Problem
Six complete wavelength intervals span 0.48 m. The same steady wave completes 24 cycles in 2.0 s. Find wavelength, frequency and speed.
Show full solution
Find one spatial interval
Method
Divide the measured distance by the number of complete wavelength intervals.
Reason
A wavelength is one repeat distance, so a longer span contains several of them.
Working
Answer
λ = 0.48 m/6 = 0.080 m.Count cycles per second
Method
Divide the number of cycles by the elapsed time.
Reason
Frequency is cycles per second, not seconds per cycle.
Working
Answer
f = 24/2.0 s = 12 Hz.Match the same wave
Method
Multiply the frequency and wavelength measured under the same conditions.
Reason
In one cycle the wave pattern advances one wavelength.
Working
Answer
v = fλ = 12 × 0.080 = 0.96 m/s. Units: Hz × m = m/s.
Quick check
Use the same steady wave and medium conditions for both measurements. A photograph alone gives spatial information, not frequency.
Try it yourself 4
Choose data that belong together
Problem
At setting A in a ripple tank, λ = 0.090 m and f = 10 Hz. After the water depth is changed, setting B has λ = 0.060 m and f = 14 Hz. A student combines A’s wavelength with B’s frequency. Calculate the speeds for each setting and choose why the mixed product is invalid.
Try before revealing the solution
Hints
Hint 1
Choose the relevant evidence
Keep each frequency with its own wavelength and medium conditions; calculate a speed for each setting.
Show solution step by step
Keep matched pairs
Method
Use each wavelength with its own measured frequency.
Reason
Changing water depth changes the wave conditions, so values from different settings need not describe the same wave speed.
Working
Answer
A: v = 10 × 0.090 = 0.90 m/s. B: v = 14 × 0.060 = 0.84 m/s.
Reject the mixed result
Method
Do not report 14 × 0.090 = 1.26 m/s as either measured speed.
Reason
The mixed product describes neither measured wave.
Working
Answer
Record setting, depth, distance, interval count and cycle timing together. If testing a frequency effect, keep depth and other relevant conditions fixed.
Quick check
The change in these supplied speeds does not show that frequency alone caused it: depth was also changed.
Check your understanding 1 Wave speed from crests and cycles
The first and fifth successive crests are 0.28 m apart. The same steady wave completes 15 cycles in 3.0 s. Find wavelength, frequency and wave speed. Choose which measurement would be missing from a single still photograph.
Show the steps Optional working
Show answer
Five crests enclose four intervals: λ = 0.28/4 = 0.070 m. Frequency is 15/3.0 = 5.0 Hz, so v = 5.0 × 0.070 = 0.35 m/s. The photograph alone does not give cycle timing or frequency. Measuring several intervals is useful only when they are counted correctly.
Common mistakes
- Dividing by the number of crests instead of the number of gaps between them.
- Timing a single cycle when timing many cycles would give a smaller percentage uncertainty.
- Combining a wavelength from one setting with a frequency from another.
- Measuring between points that are not in the same phase.
Spotted an error? Report a correction
Syllabus and review details
- SEC G3 Physics 2027 · 2027
Content Structure, PDF page 9; Subject Content, PDF pages 10–28
Last reviewed: