Question

calculate the distance between 1st node and 5th node of stationary wave in terms of λ​

Answer 1

Answer:

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 λ.

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.

2

λ

.

Hence the distance between two successive antinodes is

2

λ

.

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

4

λ

.