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Question

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


A
λ
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B
λ4
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C
λ2
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D
2λ
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Solution

The correct option is B $$\displaystyle \frac{\lambda}{4}$$
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.  $$\cfrac{\lambda}2.$$
Hence the distance between two successive antinodes is $$\cfrac{\lambda}2.$$
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 $$\cfrac{\lambda}4.$$
 

Physics

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