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Standing waves or stationary waves are an important part of physics. The node and antinode of the standing wave give a clear understanding of the amplitude and frequency dynamics during the wave superimposition. Furthermore, the difference between node and antinode gives a clear idea about their specific roles and separates them from the regular crests and troughs.
This section will cover all about the standing waves, the node and antinode of the standing wave, the antinode wave, and the difference between node and antinode. By the end of the section, students can understand all about the nodes and antinodes and can go for the quick questions to confirm their doubts.
Standing waves
A standing wave is different from a travelling wave. Instead, every point oscillates about the point of the wave’s axes in a standing wave. These adjacent points remain in phase while the points of a particular phase remain at a fixed location over time. Hence, no energy transfers from one point to the other while all adjacent points are in phase.
Hence, any standing wave is formed due to the superposition of the two travelling waves of the same frequency but in opposite directions. The travelling wave and its reflection are used to ensure the same frequency. Let us now understand about nodes and antinodes of any standing wave.
Features of the standing waves
The key features or characteristics of standing waves include:
The particles of the standing waves in the neighbouring segments vibrate in the opposition phase, while the particles of the same division vibrate in the same phase.
There is no transfer or exchange of energy during the vibration of particles.
The difference between the two consecutive nodes or antinodes is equal to half of the difference between the distance of one node and its adjacent antinode.
Node and antinode of the standing wave
Node is the position on the standing wave that remains in a fixed position over time. It is due to the destructive interference of two waves. The antinode wave is the one where particles vibrate with the maximum amplitude.
Hence, the standing wave has a maximum amplitude at the antinode while the minimum amplitude at the node. Hence, the endpoints of any standing waves are nodes. Therefore, the amplitude of the standing wave is given by: 2asin kx, where x represents the position of nodes or antinodes, and a is the amplitude.
For node:
2a sin kx = 0
sin kx = 0
sin kx = sin n
kx = n
For antinode:
2asinkx = maximum which is possible when sinkx = 1
sinkx = sin ((n + ½))
kx = n + ½
x = n + ½
Difference Between Node and Antinode
Nodes and antinodes are produced alternatively in any standing wave; however, both are different in the following ways.
Sr. No. | Node | Antinode |
1 | It represents the position of zero amplitude of the standing wave. | It represents the position of maximum amplitude of the standing wave. |
2 | The formula for amplitude is given as 2a sin kx. | The formula for amplitude is given as 2a sin kx. |
3 | Half a wavelength separates the two consecutive nodes. | These are located halfway between the pair of nodes. |
4 | The velocity and speed of particles at a node are zero. | The velocity and speed of particles at the antinode are the maxima. |
5 | The change in pressure at the node is maximum. | The change in pressure at the antinode is minimum. |
Conclusion
It is easy to understand the standing waves, nodes, and antinodes. It is easy to go through the node and antinode of the standing wave and understand the difference between them. This study of waves comes with multiple real-life applications like string instruments, woodwind instruments, etc.
After going through the basics of nodes and antinodes, it becomes easy for the students to understand the behaviour of the standing waves.
