Amplitude is how far the wave rises above the middle line, and frequency is how many complete waves pass each second. On a displacement-time graph, amplitude is the vertical reading and period is the horizontal one.
This lesson belongs to wave and image interpretation. The next lesson, on time-axis graphs, builds on it.
Which feature of the graph shows which quantity?
Amplitude is the vertical distance from the equilibrium line to a peak. Period is the horizontal distance for one full cycle. Frequency then follows from f = 1/T.
Before you read the wave, write the unit beside each axis. Displacement is in cm or m, and time is in s.
Worked example: three graphs, one change each
Wave A has peaks at +4 cm and troughs at −4 cm, and one full cycle takes 0.50 s. So its amplitude is 4 cm, its period is 0.50 s, and its frequency is 1 ÷ 0.50 = 2 Hz.
Wave B has peaks at +2 cm and the same 0.50 s cycle. Only the amplitude changed, to 2 cm. The frequency is still 2 Hz, so B is a flatter wave at the same pace.
Wave C keeps the 4 cm amplitude but one cycle takes 0.25 s. The frequency is 1 ÷ 0.25 = 4 Hz. C looks more crowded, but its height is the same as A.
| Wave | Amplitude | Period | Frequency |
|---|---|---|---|
| A | 4 cm | 0.50 s | 2 Hz |
| B | 2 cm | 0.50 s | 2 Hz |
| C | 4 cm | 0.25 s | 4 Hz |
The mistake that costs marks
The common error is to read peak to trough and call that the amplitude. For wave A that gives 8 cm instead of 4 cm.
A second slip is to say wave C is bigger because it looks busier. Crowding shows a short period, not a large amplitude. Always ask which axis the change is along: vertical means amplitude, horizontal means period.
How do you answer a written comparison?
SPM questions often ask what changed between two graphs. Name the quantity, give both values with units, and then state what stayed the same.
For A and B, a full answer is: “The amplitude decreased from 4 cm to 2 cm. The period stayed at 0.50 s, so the frequency did not change.”
Check yourself
A displacement-time graph oscillates between +5 cm and −5 cm. Six half-cycles, which means three full cycles, take 1.5 s. Find the amplitude, period and frequency.
Answer
Amplitude is 5 cm, measured from the middle line to a peak, not 10 cm.
Three full cycles in 1.5 s means one cycle takes 1.5 ÷ 3 = 0.50 s, so the period is 0.50 s.
Frequency = 1 ÷ 0.50 = 2 Hz.
What to study next
Move on to the time-axis lesson, where the same graph has to give a wavelength. The graph evidence and fair-comparison lab is useful for practising comparisons.
For help reading your own graphs, see online one-to-one Physics tuition.