Question

In stationary waves, the distance between a node and its adjacent antinode is ____.
A.\[\lambda \]
B. \[\dfrac{\lambda }{4}\]
C. \[\dfrac{\lambda }{2}\]
D. \[2\lambda \]

Answer 1

Hint: A node is defined as a point along a standing wave where the particles travelling along the wave are stationary. Here, the wave has minimum amplitude. The points that undergo the maximum displacement during each vibrational cycle of the standing wave are called antinodes.These are opposite to nodes and have no kinetic energy and maximum potential energy. So, to solve this question we have to first find the position of node and antinode and then find the distance between them.

Complete step-by-step answer:
A wave consists of crests and troughs which are the parts of the wave above and below the line of travel of the wave respectively.We also know that the distance between two successive crests or troughs is one wavelength that is one $\lambda$ .In a stationary wave, at the places where a crest or a trough is formed there the particles vibrate with the maximum amplitude above or below the line of travel. This place is known as an antinode. We know that the distance between a crest and a successive trough is half the wavelength that is \[\dfrac{\lambda }{2}\]. Hence the distance between the two successive antinodes is \[\dfrac{\lambda }{2}\]. Exactly at the centre in between two adjacent antinodes there are particles which appear to be stationary. They vibrate with minimum amplitude. This point in a wave where particles appear to be stationary are called nodes. As there lies one node exactly in between two antinodes the distance between a node and its successive antinode will be half the distance between two successive antinodes.Hence the distance between a node and its adjacent antinode is \[\dfrac{\lambda }{4}\].

So, the correct answer is “Option B”.

Note: Wavelength can be defined as the distance between two successive crests or troughs of a standing wave. It is measured in the direction of the wave. Each wave consists of 2 nodes and 2 antinodes that is one crest and one trough. A standing wave always consists of an alternating pattern of the nodes and the antinodes.