Wave Diagrams and Measurements

Wave properties can be measured from two types of graph.

Displacement-distance graph (snapshot)

This shows the displacement of particles at one instant in time.

• Wavelength ($\lambda$): the distance between two consecutive points in phase (crest to crest, trough to trough). Read from the x-axis.
• Amplitude ($A$): the maximum displacement from the equilibrium position. Read from the y-axis.

Displacement-time graph (at one point)

This shows how the displacement of ONE particle changes over time.

• Period ($T$): the time for one complete cycle (peak to next peak). Read from the x-axis.
• Amplitude ($A$): the maximum displacement. Read from the y-axis.
• Frequency: $f = 1/T$.

Key differences

Feature	Displacement-distance	Displacement-time
x-axis	Distance (m)	Time (s)
Shows	Wavelength	Period
Represents	Snapshot of all particles	History of one particle

Worked example

A displacement-time graph shows 4 complete cycles in 0.8 s.

$T = \frac{0.8}{4} = 0.2 \text{ s}$ $f = \frac{1}{0.2} = 5 \text{ Hz}$

Common errors and how to correct them

• Measuring half a wavelength (trough to crest) instead of a full wavelength (crest to crest).
• Confusing which graph gives wavelength and which gives period.
• Reading amplitude as peak-to-peak instead of peak to equilibrium.

How to apply this in an exam

Identify the graph type first. For wavelength, use the displacement-distance graph. For period/frequency, use the displacement-time graph. Measure from peak to peak or trough to trough for accuracy.