The distance between two successive trough points of a wave is

Answer Details

A wavelength \(\lambda\) is defined as the distance between any two successive points on a wave that are in phase, that is, points that are at the same stage of the vibration and moving in the same direction. Two neighbouring troughs satisfy that definition exactly: each is a point of maximum downward displacement, so the separation between them is one complete wavelength. The same is true of two neighbouring crests.

The distance that equals half a wavelength is the separation between a crest and the trough next to it, because those two points are exactly out of phase, one at maximum positive displacement and the other at maximum negative displacement. Confusing these two measurements is the usual source of error, and it matters in calculations: in a resonance-tube or standing-wave experiment the distance between consecutive nodes is \(\lambda/2\), whereas the distance between consecutive troughs of a travelling wave is \(\lambda\).

A quick check with numbers makes this secure. If \(\lambda = 0.5\,\mathrm{m}\), successive troughs are \(0.5\,\mathrm{m}\) apart and each trough is \(0.25\,\mathrm{m}\) from the crest beside it. In the examination, decide first whether the two marked points are in phase or out of phase, and only then attach \(\lambda\) or \(\lambda/2\) to the distance.