Question

In a transverse wave, the distance between a crest and the immediate trough is $\lambda /2$?

Answer 1

In a transverse wave the wavelength $\lambda$ is defined as the distance between two consecutive crests or troughs.

A trough exists in between two consecutive crests and a crest exists between two consecutive troughs.

Hence the distance between a crest and the immediate trough = half of the wavelength i.e. $\frac{\lambda }{2}$.