A standing, or stationary, wave is distinguished from a progressive wave by the fact that it does not propagate.
A standing wave results from the superposition of two progressive waves of the same frequency, but moving in opposite directions.
To understand this, let’s place an obstacle in the medium of propagation, and require that the front of the wave in contact with the obstacle, here shown in red, remains fixed.
The incident wave seems to bounce …and a standing wave arises.
And it really is a matter of bouncing.
In solving the equations for propagation, and taking into account the limiting condition imposed by the obstacle, one can demonstrate that the incident wave is totally reflected.
A sort of mirror effect.
The standing wave is precisely the sum of these two progressive waves:
The incident wave, which propagated toward positive values of x, and the reflected wave, with the same frequency and amplitude, but moving in the opposite direction.
This summing of two waves is interpreted as an interference phenomenon.
At some places, the effects add together and the amplitude is doubled. We call these points of maximum vibration “antinodes”.
At other places, the effects cancel one another out. These are the “nodes” of vibration.