A wave graph shows displacement on the vertical axis. What the horizontal axis shows decides whether the repeat length is a wavelength or a period.
This lesson is part of SPM Physics waves. It uses the quantities from relating speed, frequency and wavelength.
What do the two graphs show?
| Graph | Horizontal axis | Repeat length gives | Shows |
|---|---|---|---|
| Displacement-distance | Distance (m) | Wavelength λ | The wave frozen at one moment |
| Displacement-time | Time (s) | Period T | One point moving up and down |
Amplitude reads the same on both: the height of a crest above the centre line.
Worked example: two graphs, one wave
An original wave has a displacement-distance graph with two complete waves spanning 1.2 m, and a peak displacement of 3.0 cm.
The wavelength is 1.2 ÷ 2 = 0.60 m, and the amplitude is 3.0 cm.
The displacement-time graph of one point shows 0.25 s between neighbouring crests. The period is 0.25 s, so f = 1 ÷ 0.25 = 4.0 Hz.
Speed v = fλ = 4.0 × 0.60 = 2.4 m s⁻¹. Check with v = λ ÷ T = 0.60 ÷ 0.25 = 2.4 m s⁻¹.
The mistake that costs marks
The slip is to read 0.25 s from the time graph and call it a wavelength. Another is to read 1.2 m from the distance graph and treat it as one wavelength.
| Step | Wrong | Right |
|---|---|---|
| Wavelength | 1.2 m (whole span) | 1.2 ÷ 2 = 0.60 m |
| Quantity from time axis | Wavelength 0.25 | Period 0.25 s |
The fix is a ten-second routine: read the axis label, circle one complete wave, then count how many complete waves the span contains.
How do I count complete waves?
A complete wave runs from a point to the next identical point, such as crest to crest. Half a wave from crest to trough is not a full repeat.
If a span contains two and a half waves across 1.5 m, the wavelength is 1.5 ÷ 2.5 = 0.60 m. If the graph starts and ends on the middle line, count half waves and divide by two.
Check yourself
A displacement-time graph of a wave shows three complete cycles in 1.5 s and an amplitude of 3 cm. A displacement-distance graph for the same wave shows a wavelength of 0.50 m. Find the frequency and the wave speed.
Answer
Period T = 1.5 ÷ 3 = 0.50 s, so f = 1 ÷ 0.50 = 2.0 Hz.
v = fλ = 2.0 × 0.50 = 1.0 m s⁻¹.
The amplitude of 3 cm is not needed for the speed.
What to study next
For more practice with labelled diagrams, see wave and image interpretation with labelled diagrams. Then test the chapter in the waves practice set.
If you want a teacher to train the axis-checking habit, see online one-to-one Physics tuition.