← Oscillations and wave anatomy

What amplitude is

Two mornings at the same dock. Monday's ripples barely tickle the posts. Saturday's waves ride high above the calm level and slap them hard. Beata wants one number that says how big a wave is.

The number physics uses is a height, but measured from a particular place. Measured from the wrong place, it comes out double. This lesson pins it down.

Earlier in the course, displacement meant how far something sits from its rest position. The word keeps that meaning here.

As a wave passes, each bit of the medium's displacement grows and shrinks. Its largest value happens at a crest top or a trough bottom.

rest positioncresttrough
The ripple rises above its rest level and dips below it. How big is it, in one number?
The maximum displacement of the medium from its rest position is called the wave's amplitude. Amplitude is measured from the rest position to a crest, never from a crest to a trough.

A ripple whose crests rise 2 cm above the flat rest level has an amplitude of 2 cm.

rest positionamplitude: 2 cm
Measured from the rest line to the crest: the amplitude, 2 cm.

The crest-to-trough height of that ripple is 4 cm: twice the amplitude. Measuring crest to trough is the classic mistake.

The 2 cm ripple, read two waysmeasurementvalueis it the amplitude?rest level to crest top2 cmyescrest top to trough bottom4 cmno: twice the amplitude
Same ripple, two reads: only the rest-to-crest read is the amplitude.

From here on, every amplitude arrow in this topic runs from the rest line to a crest.

rest positionamplitude: 6 cm
A second wave, the same measure: rest line to crest, 6 cm.

Swells lift a harbor's surface 4 cm above its calm rest level at each crest. State the amplitude.

The amplitude is the maximum displacement from the rest position.

Each crest sits 4 cm above the rest level.

The amplitude is 4 cm.

A snapshot of a rope wave shows the vertical distance from a trough bottom to a crest top is 12 cm. Find the amplitude.

Crest-to-trough spans twice the amplitude: from one maximum displacement, through the rest line, to the other.

12 ÷ 2 = 6

The amplitude is 6 cm, measured from the rest line to the crest.

A snapshot of a pool wave shows the vertical distance from a trough bottom to a crest top is 6 cm. Enter the wave's amplitude in cm.

A rope wave has an amplitude of 2.5 cm. Enter the vertical distance, in cm, from one of its trough bottoms to a crest top.

Dilys compares two rope waves in a snapshot. She says: 'The wave whose crests rise higher above the rest line has the larger amplitude.' Is Dilys correct?

Your turn

A wave snapshot carries four marked arrows. Which arrow shows the wave's amplitude?

JKLM

A wave tank's screen shows the vertical distance from a trough bottom to a crest top is 16 cm. Enter the wave's amplitude in cm.

Anselm measures a rope wave from a crest top straight down to the trough bottom and calls that distance the amplitude. Beata measures from the rest line up to the crest top and calls that the amplitude. Who measured the amplitude correctly?