The vocabulary of a wave

By the end of this lesson

By the end you can define displacement, amplitude, wavelength, period, frequency and speed, and read the first four from a displacement–distance or displacement–time graph.

Key to the symbols

The main symbols used in this lesson:

Symbol	Meaning
$\lambda$	wavelength
$A$	amplitude
$f$	frequency
$v$	speed of the wave

Two different snapshots

A wave can be photographed in two ways, and mixing them up causes most of the confusion in this topic.

Displacement against distance is a photograph of the whole wave at one instant. It shows the shape of the wave along the medium.

Displacement against time is a video of one point. It shows how a single particle moves as the wave goes past.

Both graphs look like sine waves. They are not the same graph.

Graph	Horizontal axis	What one full cycle gives you
Displacement–distance	distance along the medium	wavelength $\lambda$
Displacement–time	time at one point	period $T$

Definition

The key terms

Displacement $x$ : the distance of a point from its equilibrium position, in a stated direction. It is a vector, so it can be positive or negative.
Amplitude $A$ : the maximum displacement from equilibrium. Always positive.
Wavelength $\lambda$ : the distance between two consecutive points that are in phase — for example crest to crest, or trough to trough.
Period $T$ : the time for one complete oscillation of a point, or the time for the wave to travel one wavelength.
Frequency $f$ : the number of complete oscillations per unit time. Measured in hertz (Hz), where $1\ \text{Hz} = 1\ \text{s}^{-1}$ .
Speed $v$ : the distance travelled by the wave pattern per unit time.

Period and frequency are reciprocals:

$f = \frac{1}{T} \qquad T = \frac{1}{f}$

Amplitude is not the height of the wave

The height of a water wave is often quoted as the vertical distance from trough to crest. That is twice the amplitude.

Amplitude is measured from the equilibrium line to a crest (or to a trough), not from the bottom to the top.

This matters in calculations. If a question says a wave has amplitude $0.15\ \text{m}$ , the crest is $0.15\ \text{m}$ above equilibrium and the trough is $0.15\ \text{m}$ below it.

The same trap appears on an oscilloscope: the peak voltage is the amplitude, while the peak-to-peak voltage is twice that.

Worked example: Worked example: reading a snapshot

A displacement–distance graph shows crests at $0.20\ \text{m}$ and $0.68\ \text{m}$ from the source, and the wave has amplitude $0.040\ \text{m}$ .

Find the wavelength and the distance from a crest to the nearest trough.

Have a go first?

Worked example: Worked example: from period to frequency

A point on a wave completes one oscillation in $0.025\ \text{s}$ .

Find the frequency of the wave.

Have a go first?

Quick check

Multiple choiceQuestion 1 · Recall

CalculateQuestion 2 · Recall

CalculateQuestion 3 · Recall

Answer the 3 questions above to continue.