← Oscillations and wave anatomy

Crest and trough

Beata watches ripples slide past a dock post. Each ridge of water rides a little above the flat level the pond had before, and between the ridges the surface dips a little below it.

Transverse waves have a shape, and the shape has two landmarks. This lesson names them.

The pond's flat, undisturbed level is drawn as a dashed line: the rest position of the surface.

The wave's shape rises above that line and dips below it, over and over.

rest position
The ripple snapshot about its dashed rest position: it rises above the line and dips below it, over and over.
The highest point of the wave above the rest position is called a crest. The top of each water ridge is a crest. The lowest point of the wave below the rest position is called a trough.
rest positioncrest
The highest point above the rest position: a crest.
rest positioncresttrough
The lowest point below the rest position: a trough.

Crests and troughs alternate along the wave: crest, trough, crest, trough.

A point sitting ON the rest line, between a crest and a trough, is neither: crest and trough name only the highest and lowest points.

rest positioncresttroughR(neither)
A fresh wave, the same landmarks; a point on the rest line is neither a crest nor a trough.

These two landmarks come up in every transverse-wave lesson from here on, so check them against the rest line every time.

A snapshot of a rope wave marks point J at the top of a rise, highest above the dashed rest line. What is J?

J sits highest above the rest position.

The highest point above the rest position is a crest.

J is a crest.

The same snapshot marks point K at the bottom of the dip beside J, lowest below the rest line. What is K?

K sits lowest below the rest position.

The lowest point below the rest position is a trough.

K is a trough.

The snapshot of a lake swell marks three points: J, K, and L. Which letter marks a crest?

JKL

The snapshot of a rope wave marks three points: M, N, and P. Which letter marks a trough?

MNP

Anselm looks at a wave snapshot and says: 'Every crest on this wave sits above the rest line, and every trough sits below it.' Is Anselm correct?

Your turn

Which statement about the crests of a transverse wave is correct?

A swell snapshot marks four points: Q at a highest point, R on the rest line, S at a lowest point, and T halfway up a rise. Which letter marks a trough?

QRST

Point R sits exactly on the rest line of a wave snapshot, halfway between a crest and a trough. What is R?