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Lesson · Physics

Amplitude or frequency: what changed on the graph?

Two wave graphs look different, and you are not sure which quantity actually changed.

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.

Common questions

Is amplitude the distance from the top of a wave to the bottom?

No. Amplitude is the maximum displacement from the rest (equilibrium) position, so it is measured from the middle line to a peak. The distance from trough to crest is the peak-to-peak value, which equals twice the amplitude.

How do I find frequency from a displacement-time graph?

Read the period T, the time for one complete oscillation, from the time axis. Then use f = 1/T. Always state the unit, hertz (Hz) for frequency and seconds (s) for period.

Does a taller wave have a higher frequency?

No. Height shows amplitude, which links to the energy of the wave. Frequency depends on how many complete waves fit in each second, so it is read from the horizontal spacing, not the height.

What if the graph starts at a trough instead of the middle?

The starting point does not change period or amplitude. Count one full cycle from any point back to the same point with the same direction, such as trough to the next trough.

If graph questions still feel like guesses in a timed test, one-to-one Physics lessons let a teacher watch you read a graph aloud and catch the exact step where the wrong quantity gets chosen.

  • Online one-to-one lessons for your child with an experienced teacher.
  • Your first class is a one-hour trial, from RM50. The fee is agreed before you book.
  • Happy with the teacher? Continue with lessons of about 1.5 hours. If not, ask for another teacher.