Difference Between Node and Antinode

Different from a travelling wave is a standing wave. A standing wave forms where each point oscillates about the wave's axes. While the points of a specific phase remain at a constant location across time, these nearby points continue to be in phase. Since all nearby points are in phase, no energy is transferred between them.

The superposition of two travelling waves of the same frequency but going in opposite directions results in the formation of standing wave. To guarantee the same frequency, the travelling wave and its reflection are employed. Let's discuss the nodes and antinodes of a standing wave.

Characteristics of Stationary Waves: 

The primary traits or qualities of standing waves are as follows:

• Standing wave particles in adjacent segments vibrate in the opposite phase from those in the same division, who vibrate in the same phase.

• Particle vibration does not involve any energy transfer or exchange.

• Half of the distance between one node and its adjacent antinode is the difference between two successive nodes or antinodes.

Antinode and Node of the Standing Wave: 

The spot on a standing wave known as a node stays in place over time at a fixed position. Due to two waves interfering destructively, this is the cause. The wave where particle vibration is at its strongest is called the antinode wave.

The standing wave therefore has its largest amplitude at the antinode and its minimum amplitude at the node. Any standing wave's endpoints are called nodes for this reason.

Nodes and Antinodes on a Standing Wave

Formula for Finding Position of Nodes and Antinodes on a Standing Wave: 

For Antinodes:

$2a\sin \left (kx\right )=1$ 

$sinkx = sin \left ( \left ( n + 1/2 \right )\pi/2 \right )$ 

$kx = \left (n + 1/2 \right )\pi/2$

$x = \left ( n + 1/2 \right )\lambda/2$

For n=0,1,2,...

Where, a= amplitude of the wave

k= wave propagation constant

\lambda= wavelength

For Nodes:

$2a\sin \left (kx\right )=0$

$\sin \left (kx\right )=0$

$\sin \left (kx\right )= \sin\left ( n\pi  \right )$

$kx=n\pi$

$x=n\lambda$

For n=0,1,2,...

Where a= amplitude of the wave

k= wave constant

Differentiate Between Node and Antinode of a Standing Wave: 

Summary 

Standing waves, nodes, and antinodes are simple to comprehend and can be better understood through node and antinode examples. The standing wave's node and antinode are simple to examine and distinguish from one another. Numerous practical applications, such as those in woodwind and string instruments, are available for this study of waves. The readers will find it simple to comprehend the standing wave behaviour once they have gone over the fundamentals of nodes and antinodes along with how to differentiate between node and antinode.