Question

In stationary wave, the distance between a node and its adjacent antinode is __________.

• A. $\lambda$
• B. $\frac{\lambda }{4}$
• C. $\frac{\lambda }{2}$
• D. $2\lambda$

Answer 1

The correct option is B $\frac{\lambda }{4}$

Let us consider a transverse wave for convenience, although this point is applicable for longitudinal wave also.

We know that a transverse wave consists of crests and troughs.

We also know that the distance between two successive crests or troughs is one wavelength i.e. one $\lambda .$

In a stationary wave, at the places where a crest or a trough is formed, the particles vibrate with maximum amplitude. Such a place is called an antinode.

We know that the distance between a crest and a successive trough is half wavelength i.e. $\frac{\lambda }{2}.$

Hence the distance between two successive antinodes is $\frac{\lambda }{2}.$

Exactly at the centre in between two adjacent antinodes there are particles which appear to be stationary. They vibrate with minimum amplitude.

Hence the distance between a node and its adjacent antinode is $\frac{\lambda }{4}.$