Wavelength and Amplitude - Waves, Oscillations, and Resonance Step by Step

Amplitude is the crest height and wavelength is the crest-to-crest distance, both read straight off the frozen wave picture.

waves Clean A = 1 m and wavelength = 3 m are read directly off the snapshot.

Example

Amplitude is the crest height and wavelength is the crest-to-crest distance — both read straight off the frozen wave picture. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Amplitude: how far from the middle

The amplitude is the greatest displacement from the rest line — the height of a crest. Here the string rises 1 metre above the middle at each crest, so the amplitude is 1 metre.

A = \hl{1}\ \text{m}

Larger amplitude means a taller wave

Amplitude is measured from the middle to a crest. The full crest-to-trough height is twice the amplitude, so larger amplitude makes the whole up-down motion larger.

\begin{array}{c|c|c}A & \text{crest height} & \text{crest-to-trough} \\ \hline 1\ \text{m} & 1\ \text{m} & 2\ \text{m} \\ 2\ \text{m} & 2\ \text{m} & 4\ \text{m} \\ 3\ \text{m} & 3\ \text{m} & 6\ \text{m}\end{array}

Wavelength: one full cycle in space

The wavelength is the distance over which the wave repeats — from one crest to the next. Reading the snapshot, successive crests are 3 metres apart, so the wavelength is 3 metres.

\lambda = \hl{3}\ \text{m}

More cycles take more distance

Hold wavelength fixed. Each complete cycle occupies one wavelength in the snapshot, so more cycles take proportionally more distance along the string.

\begin{array}{c|c|c}\text{cycles} & \lambda & \text{distance} \\ \hline 1 & 3\ \text{m} & 3\ \text{m} \\ 2 & 3\ \text{m} & 6\ \text{m} \\ 3 & 3\ \text{m} & 9\ \text{m}\end{array}