Graphical Representation of a Wave
Simple Explanation
A wave can be shown on a graph two ways: a displacement-DISTANCE graph, which is like a snapshot of the wave at one instant (showing wavelength directly), or a displacement-TIME graph, which shows how one single point moves over time (showing period directly). Both types of graph show amplitude as the height of the peaks.
Why Do We Need It?
Being able to read a wave graph correctly — and knowing which type you are looking at — is essential, since a displacement-distance graph and a displacement-time graph can look identical but represent completely different information.
See It
A sine curve showing a wave pattern, with peaks and troughs representing the maximum positive and negative displacement
Worked Example
Read wavelength and amplitude off a displacement-distance graph
A displacement-distance graph shows a wave with peaks at 0 m, 4 m, and 8 m, and a maximum height (above the rest position) of 3 cm. Find the wavelength and amplitude.
Why Does This Work?
A displacement-distance graph literally plots the shape of the wave at a frozen instant, so the physical distance between two identical points (like consecutive peaks) directly IS the wavelength, and the peak height directly IS the amplitude — no calculation needed, just careful reading.
Real-Life Example
An oscilloscope trace of a sound wave
An oscilloscope connected to a microphone displays a sound wave as a displacement-TIME graph.
Reading the time between successive peaks on this screen gives the sound's period directly, from which frequency (f = 1/T) can be found — exactly how sound engineers analyze audio signals.
Practice
A displacement-TIME graph (for a single point on a wave) shows successive peaks 0.02 s apart. What does this 0.02 s represent?
MediumCommon mistake
Confusing a displacement-distance graph with a displacement-time graph — reading a wavelength off a displacement-TIME graph (or a period off a displacement-DISTANCE graph) gives a value with completely the wrong meaning and units.
Quick Review
- Displacement-distance graph: a snapshot in space, shows wavelength.
- Displacement-time graph: tracks one point over time, shows period.
- Both types show amplitude as the peak height.