6.5 Displacement Graphs and Waveforms

Displacement vs. Position vs. Time

A displacement-position graph freezes the wave at one instant, showing how particle displacement varies along the medium — its horizontal distance gives wavelength (λ). A displacement-time graph tracks one point in the medium over time, showing how it oscillates — its horizontal distance gives period (T). Both are sine-shaped, but they measure completely different axes.

Reading amplitude and quantities from graphs

The amplitude (A) is the maximum vertical displacement from equilibrium on either graph. From a position graph, measure λ directly. From a time graph, measure T, then find frequency f = 1/T. Combining both graphs (or using v = fλ) lets you find wave speed even if only one graph is given directly.

Transverse vs. longitudinal waveforms

For transverse waves, the displacement graph directly resembles the physical wave shape. For longitudinal waves (like sound), displacement is parallel to propagation, so the graph shows particle displacement (compressions/rarefactions) as peaks and troughs even though particles move back-and-forth along the travel direction, not up-and-down.

Key terms

Displacement-position graph

A snapshot of the wave showing displacement vs. location; horizontal distance between peaks = wavelength.

Displacement-time graph

Tracks one particle's displacement over time; horizontal distance between peaks = period.

Amplitude (A)

Maximum displacement from equilibrium, shown as peak height on either graph.

Frequency from period

f = 1/T, calculated from the period read off a displacement-time graph.

Longitudinal wave displacement graph

Shows particle displacement parallel to propagation as a sine curve, even though motion isn't up-and-down like the graph appears.

Try an AP-style question

On a displacement vs. position graph of a wave, what does the distance between neighboring crests show?

1. The amplitude
2. The frequency
3. The period
4. The wavelength