Crest-Trough Half-Wavelength Three-Row Scan - Waves & Sound Step by Step

Three spatial wave rows show that crest-to-trough distance is half the wavelength, not a full repeat.

Example

Crest-to-trough spacing is half a wavelength, so the geometry scales with the wavelength row. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Crest-to-trough distance is half a wavelength

A crest and the nearest trough are not one full repeat apart. They are half a cycle apart, so their spacing is half the wavelength.

\text{crest to trough}=\lambda/2

Short wavelength row

With wavelength 2 m, crest-to-trough spacing is 1 m.

\text{crest to trough}=\frac{\lambda}{2}=\frac{2\ \text{m}}{2}=1\ \text{m}

Middle wavelength row

With wavelength 4 m, crest-to-trough spacing is 2 m.

\text{crest to trough}=\frac{\lambda}{2}=\frac{4\ \text{m}}{2}=2\ \text{m}

Long wavelength row

With wavelength 6 m, crest-to-trough spacing is 3 m.

\text{crest to trough}=\frac{\lambda}{2}=\frac{6\ \text{m}}{2}=3\ \text{m}

Half-wavelength spacing scales with wavelength

The diagram spacing grows with wavelength, and the table keeps the half-cycle distance pinned in metres.

\begin{array}{c|c}\lambda & \text{half wavelength} \\ \hline 2\ \text{m} & 1\ \text{m} \\ 4\ \text{m} & 2\ \text{m} \\ 6\ \text{m} & 3\ \text{m}\end{array}

waves Wavelengths 2 m, 4 m, and 6 m give crest-to-trough spacings 1 m, 2 m, and 3 m.