Reading graphs of transverse and longitudinal waves

By the end of this lesson

By the end you can read amplitude and wavelength from a displacement–distance graph, read period from a displacement–time graph, and explain why a graph of a longitudinal wave is a plot rather than a picture.

Key to the symbols

The main symbols used in this lesson:

Symbol	Meaning
$\lambda$	wavelength

One kind of graph is a photograph

Take a wave on a rope and photograph it. What you see is a wavy line: up, down, up, down along the rope.

Plot displacement against distance for that moment and you get the same wavy line. For a transverse wave, the displacement–distance graph is the shape of the wave.

That is not true for sound. You cannot photograph a compression. Sound is a pattern of squeezes inside the air, and a graph of it can only plot numbers: how far each particle has been pushed from its rest position, and in which direction.

So the same sine curve can mean two very different things. Always check which wave you are reading about.

The upper graph is what the wave looks like. The lower graph is a set of measurements of particle displacements.

What you can read from each graph

Graph	Horizontal axis	Gives you
Displacement–distance	distance along the wave	wavelength $\lambda$ and amplitude $A$
Displacement–time	time at one fixed point	period $T$ and amplitude $A$

Amplitude is measured from the equilibrium line to a crest, or to a trough. It is never crest-to-trough, which is $2A$ .

Wavelength is the distance between two consecutive points that are in phase: crest to crest, trough to trough, or from one zero crossing with a rising slope to the next zero crossing with a rising slope. For a longitudinal wave it is also the distance from one compression to the next.

Frequency is not on either graph directly. Get it from $f = 1/T$ after reading the period.

Displacement–time graphs cannot tell the two apart

Watch one air particle in a sound wave and plot its displacement against time. You get a sine curve.

Watch one point on a rope and do the same. You get a sine curve too.

The two graphs are indistinguishable. A displacement–time graph tells you the period, the amplitude and the frequency, but not whether the wave is transverse or longitudinal. For that you need to know what the wave is travelling through, or you need a displacement–distance graph where you also know what the medium is doing.

Quick check

CalculateQuestion 1 · Recall

Multiple choiceQuestion 2 · Apply

Multiple choiceQuestion 3 · Apply

Answer the 3 questions above to continue.