A time axis gives you the period, not the wavelength. To reach the wavelength you first turn the period into a frequency, then combine it with the wave speed using v = fλ.
This lesson follows amplitude and frequency on a graph. The formula itself is explained in relating speed, frequency and wavelength.
What does each kind of axis give you?
A displacement-distance graph has length on the horizontal axis, so one full wave on it is the wavelength λ. A displacement-time graph has time on that axis, so one full wave is the period T.
The two graphs can look identical. Only the axis label tells you which quantity you are reading, so read it before anything else.
Worked example: from graph to wavelength
A displacement-time graph of a sound wave shows 4 complete oscillations between t = 0 and t = 0.080 s. The speed of sound in the room is 340 m/s. Find the wavelength.
- Period: T = 0.080 ÷ 4 = 0.020 s.
- Frequency: f = 1 ÷ 0.020 = 50 Hz.
- Wavelength: λ = v ÷ f = 340 ÷ 50 = 6.8 m.
Check the units: m/s divided by Hz, which is 1/s, leaves metres. The answer is a length, as it should be.
The mistake that costs marks
The tempting error is to see one wave spanning 0.020 on the horizontal axis and write “wavelength = 0.020”. The number is real, but it is a time in seconds, not a distance.
| Step | Wrong | Right |
|---|---|---|
| Read one cycle | 0.020 called wavelength | 0.020 s is the period |
| Unit | m (assumed) | s, then convert with v |
| Final answer | 0.020 m | 6.8 m |
Does the same idea work for water waves?
Yes. Take a ripple tank wave with speed 0.30 m/s and a period of 0.50 s on the graph. The frequency is 2 Hz, so λ = 0.30 ÷ 2 = 0.15 m.
The answer is 0.15 m, which is 15 cm. If the question asks for centimetres, convert once more. Write the unit on every line to avoid losing it.
Check yourself
A displacement-time graph shows 6 complete oscillations in 0.15 s. The wave travels at 12 m/s. Find the period, frequency and wavelength.
Answer
Period: T = 0.15 ÷ 6 = 0.025 s.
Frequency: f = 1 ÷ 0.025 = 40 Hz.
Wavelength: λ = 12 ÷ 40 = 0.30 m. Check: 40 Hz × 0.30 m = 12 m/s, which matches the given speed.
What to study next
Continue with the lens sign convention lesson. The units and significant-figure checker helps you test your final answers.
To work through graph questions with a teacher, see online one-to-one Physics tuition.